transformations

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					1.

                                            y
                                            6

                                            5

                                            4

                                            3

                                            2

                                            1

                                            0
                              –2   –1                1   2       3       4       5   6     7   8 x
                                            –1

                                            –2



      (a)    Draw the line y = 2 on the grid above.
                                                                                                                 (1)

      (b)    Reflect the shaded triangle in the line y = 2.
                                                                                                                 (1)
                                                                                                     (Total 2 marks)

2.    (a)

                              y
                              6

                              5

                              4

                              3

                              2

                              1

                              0
                    –2   –1             1        2   3       4       5       6   7   8 x
                              –1

                              –2



             (i)    Draw the line y = 2 on the grid above.
                                                                                                                 (1)

             (ii)   Reflect the shaded triangle in the line y = 2.
                                                                                                                 (1)


Blessed Trinity RC College                                                                               1
      (b)

                                                     y
                                                     5

                                                     4

                                                     3

                                                     2

                                                     1

                                                                                              x
                    –6   –5    –4    –3   –2    –1 0         1    2       3   4       5   6
                                                   –1

                                                    –2

                                                    –3

                                                    –4



             (i)     Translate the shaded triangle by the vector  5 
                                                                  – 4
                                                                  

                     Label this triangle C.
                                                                                                               (2)

             (ii)    Rotate the shaded triangle through 90° clockwise about (1, 1)

                     Label this triangle D.
                                                                                                               (2)
                                                                                                  (Total 6 marks)




Blessed Trinity RC College                                                                             2
3.

                                                         y
                                                         5

                                                         4

                                                         3

                                                         2

                                                         1

                                                                                          x
                        –6   –5       –4   –3   –2   –1 0         1   2   3   4   5   6
                                                        –1

                                                        –2

                                                        –3

                                                        –4




             Translate the shaded triangle by the vector  
                                                            5
      (a)                                                 – 4
                                                          

             Label this triangle C.
                                                                                                          (2)

      (b)    Rotate the shaded triangle through 90° clockwise about (1, 1)

             Label this triangle D.
                                                                                                          (2)
                                                                                              (Total 4 marks)




Blessed Trinity RC College                                                                        3
4.    The diagram shows two identical shapes, A and B.

                                                                                     y
                                                                                     6

                                                                                     5

                                                                                     4

                                                                                     3
                                                    B
                                                                                     2

                                                                                     1


                         –6        –5        –4         –3        –2        –1 O                  1         2          3         4         5           6 x
                                                                                   –1

                                                                                   –2
                                                                                                                            A
                                                                                   –3

                                                                                   –4

                                                                                   –5

                                                                                   –6



      Describe fully the single transformation which takes shape A to shape B.

      ..............................................................................................................................................

      ..............................................................................................................................................

      ..............................................................................................................................................
                                                                                                                                                             (Total 3 marks)




Blessed Trinity RC College                                                                                                                                       4
5.    (a)

                                                                            y
                                                                            6

                                                                            5

                                                                            4
                                             A
                                                                            3

                                                                            2

                                                                            1


                            –5        –4         –3        –2        –1 O                 1          2         3         4          5 x
                                                                          –1

                                                                          –2

                                                                          –3

                                                                          –4



             (i)    Describe fully the single transformation that takes the shaded triangle to triangle A.

                    ...........................................................................................................................

                    ...........................................................................................................................
                                                                                                                                                      (2)



             (ii)   On the grid above translate the shaded triangle by 2 squares to the right and 4 squares down.
                                                                                                                                                      (1)




Blessed Trinity RC College                                                                                                                        5
      (b)    Triangle P is an enlargement of the shaded triangle.

                                                         y
                                                         6

                                                         5

                                                         4

                                                         3

                                                         2

                                                         1
                                                             P
                         –5    –4    –3     –2    –1 O             1       2         3        4        5 x
                                                      –1

                                                      –2

                                                      –3

                                                      –4



             (i)    What is the scale factor of the enlargement?

                                                             Answer ............................................................
                                                                                                                                        (1)



             (ii)   What is the centre of enlargement?

                                                             Answer (..........................., .............................)
                                                                                                                                        (1)
                                                                                                                            (Total 5 marks)




Blessed Trinity RC College                                                                                                         6
6.    Triangle P is an enlargement of the shaded triangle.

                                                       y
                                                       6

                                                       5

                                                       4

                                                       3

                                                       2

                                                       1
                                                             P
                         –5   –4     –3    –2     –1 O           1       2         3        4        5 x
                                                     –1

                                                     –2

                                                     –3

                                                     –4



      (a)    What is the scale factor of the enlargement?

                                                                 Answer ......................................................
                                                                                                                                      (1)



      (b)    What is the centre of enlargement?

                                                                  Answer (........................, ........................)
                                                                                                                                      (1)
                                                                                                                          (Total 2 marks)




Blessed Trinity RC College                                                                                                       7
7.    Triangle A has vertices (1,2), (1,5) and (3,2).

                                                          y
                                                         6

                                                         5

                                                         4

                                                         3          A

                                                         2

                                                         1


                  –6     –5    –4     –3    –2     –1 O        1        2   3      4     5      6   x
                                                        –1

                                                        –2

                                                        –3

                                                        –4

                                                        –5

                                                        –6



      Draw the new position of triangle A after a rotation of 90° clockwise about the origin.
                                                                                                        (Total 3 marks)




Blessed Trinity RC College                                                                                  8
8.    The grid shows several transformations of the shaded triangle.

                                                                       y
                                                                      5

                                                                      4

                                                                      3
                                                            C                                          A
                                                                      2

                                                                      1
                                                   D

                             –5    –4     –3           –2           –1 O   1       2       3       4           5x
                                                                     –1
                                                                                       B
                                                                     –2
                                               F                G              H                           E
                                                                     –3

                                                                     –4



      (a)    Write down the letter of the triangle

             (i)     after the shaded triangle is reflected in the line x = 3,

                                                                               Answer ............................................
                                                                                                                                          (1)

             (ii)    after the shaded triangle is translated by 3 squares to the right and 5 squares down,

                                                                               Answer ............................................
                                                                                                                                          (1)

             (iii)   after the shaded triangle is rotated 90° clockwise about O.

                                                                               Answer ............................................
                                                                                                                                          (1)

      (b)    Describe fully the single transformation which takes triangle F onto triangle G.

             ...............……………………………………………………………………………..

             ...............……………………………………………………………………………..
                                                                                                                                          (2)
                                                                                                                              (Total 5 marks)




Blessed Trinity RC College                                                                                                           9
9.    The diagram shows shape A.

                                        y


                                       10

                                        9

                                        8

                                        7

                                        6

                                                                         A
                                        5

                                        4

                                        3

                                        2

                                        1


                  –4     –3   –2   –1 O          1        2    3     4       5    6     7      8   x
                                       –1

                                       –2



                                                          1
      Draw the enlargement of shape A with scale factor     and centre of enlargement (0,0).
                                                          3
                                                                                                   (Total 2 marks)




Blessed Trinity RC College                                                                             10
10.   The diagram shows a shaded flag.

                                                          y
                                                         6

                                                         5

                                                         4

                                                         3

                                                         2

                                                         1


                                                                                                 x
                   –6        –5   –4   –3    –2     –1 O           1   2      3      4   5   6
                                                        –1

                                                        –2

                                                        –3

                                                        –4

                                                        –5

                                                        –6



      (a)    Rotate the shaded flag 90° anticlockwise about the origin.
             Label this new flag with the letter A.
                                                                                                                 (3)



      (b)    Reflect the original shaded flag in the line y = 1.
             Label this new flag with the letter B.
                                                                                                                 (2)

      (c)    Rotate the original shaded flag by a quarter-turn clockwise about (0, 2).
             Label this new flag with the letter C.
                                                                                                                 (2)
                                                                                                     (Total 7 marks)




Blessed Trinity RC College                                                                              11
11.

                                                        y
                                                        6

                                                        5

                                                        4

                                                        3

                                                        2

                                                        1


                  –6     –5    –4     –3     –2     –1 O                                            x
                                                                1      2     3     4      5     6
                                                       –1

                                                       –2

                                                       –3

                                                       –4

                                                       –5

                                                       –6
      (a)    Reflect the shaded triangle in the line y = –x.
             Label this new triangle with the letter A.
                                                                                                                    (2)

      (b)    Rotate the original shaded triangle by a quarter-turn anticlockwise about (0,2).
             Label this new triangle with the letter B.
                                                                                                                    (2)
                                                                                                        (Total 4 marks)




Blessed Trinity RC College                                                                                 12
12.   The diagram shows two triangles A and B.
                           y


                            5

                            4

                            3
                                                                              B
                            2                                                                                         A

                            1

                            0
                                                                                                                                          x
                                0           1       2         3         4          5           6       7          8           9



      Describe fully the single transformation that maps triangle A onto triangle B.

      ...............................................................................................................................................

      ...............................................................................................................................................

      ...............................................................................................................................................
                                                                                                                                                        (Total 3 marks)

13.   The diagram shows two triangles A and B.
                                    y


                                    5

                                    4

                                    3
                                                                                       B
                                    2                                                                                         A

                                    1

                                    0
                                                                                                                                                 x
                                        0       1         2         3          4           5       6          7           8       9

      (a)       Describe fully the single transformation that maps triangle A onto triangle B.

                .....................................................................................................................................

                .....................................................................................................................................

                .....................................................................................................................................
                                                                                                                                                                    (3)

      (b)       On the diagram draw the image of triangle B after it is reflected in the line y = x
                                                                                                                                                                    (2)
Blessed Trinity RC College                                                                                                                                 13
14.   The grid shows two triangles.

                                                                                y
                                                                               5

                                                                               4

                                                                               3

                                                                               2

                                                                               1


                               –5        –4        –3         –2         –1 O                1          2         3         4         5 x
                                                                             –1
                                                                                                 A
                                                                             –2

                                                                             –3

                                                                             –4

                                                                             –5

      (a)    Describe fully the single transformation that maps the shaded triangle onto triangle A.

             .....................................................................................................................................

             .....................................................................................................................................
                                                                                                                                                                 (3)

      (b)    Reflect the shaded triangle in the line x = –1
                                                                                                                                                                 (2)
                                                                                                                                                     (Total 5 marks)




Blessed Trinity RC College                                                                                                                              14
15.   The diagram shows four shapes, A, B, C and D.




                                                            6

                                                            5
                                                                              B
                                                            4

                                                            3

                                                            2
                                    C                                                                          A
                                                            1


                     –4        –3        –2         –1 O                 1          2         3         4          5         6         7             8
                                                          –1

                                                          –2

                                                          –3                                                             D

                                                          –4



      (a)    Describe fully the single transformation that takes shape A onto shape B.

             .....................................................................................................................................

             .....................................................................................................................................

             .....................................................................................................................................
                                                                                                                                                                     (2)



      (b)    Describe fully the single transformation that takes shape B onto shape C.

             .....................................................................................................................................

             .....................................................................................................................................

             .....................................................................................................................................
                                                                                                                                                                     (3)

      (c)    Describe fully the single transformation that takes shape C onto shape D.

             .....................................................................................................................................

             .....................................................................................................................................

             .....................................................................................................................................
                                                                                                                                                                     (3)
                                                                                                                                                         (Total 8 marks)

Blessed Trinity RC College                                                                                                                                  15
16.
                                                                                 y


                                                                                5

                                                                                4

                                                                                3

                                                                                2
                                                                                                                       A
                                                                                1


                     –6        –5         –4        –3        –2         –1 O                 1         2          3         4          5            6         x

                                                                              –1

                                                                              –2

                                                                              –3
                                                          C                                                            B
                                                                              –4

                                                                              –5



      (a)    Describe the transformation that maps triangle A to triangle B.

             .....................................................................................................................................

             .....................................................................................................................................

             .....................................................................................................................................
                                                                                                                                                                          (2)

      (b)    Triangle C is an enlargement of triangle A.

             (i)       Write down the scale factor of the enlargement.

                                                                                          Answer ........................................................
                                                                                                                                                                          (1)

             (ii)      Write down the coordinates of the centre of the enlargement.

                                                                                               Answer                            (...............,...............)
                                                                                                                                                                          (1)
                                                                                                                                                              (Total 4 marks)




Blessed Trinity RC College                                                                                                                                           16

				
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posted:2/11/2013
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