Quiz
Determine the slope of each line.
1. PQ
2. MN
3. Which pair of lines are parallel?
In the figure, WXYZ @ ABCD
4. Find XY.
5. Find mB.
Transformations
5.7
Pre-Algebra
Warm Up
Determine if the following sets of points form a
parallelogram.
1. (–3, 0), (1, 4), (6, 0), (2, –4) yes
2. (1, 2), (–2, 2), (–2, 1), (1, –2) no
3. (2, 3), (–3, 1), (1, –4), (6, –2) yes
Learn to transform plane figures using
translations, rotations, and reflections.
Vocabulary
transformation
translation
rotation
center of rotation
reflection
image
When you are on an amusement park ride,
you are undergoing a transformation. Ferris wheels
and merry-go-rounds are rotations. Free fall rides
and water slides are translations. Translations,
rotations, and reflections are type of
transformations.
The resulting figure or image, of a translation,
rotation or reflection is congruent to the original
figure.
Example: Identifying
Transformations
Identify each as a translation, rotation,
reflection, or none of these.
A. B.
reflection rotation
Example: Identifying
Transformations
Identify each as a translation, rotation,
reflection, or none of these.
C. D.
none of the these translation
Try This
Identify each as a translation, rotation,
reflection, or none of these.
A. B. A B
A A’
D C
D’ C’
C B’ A’ B’
B C’
translation reflection
Try This
Identify each as a translation, rotation, reflection,
or none of these.
E’
C. A’ D.
F’
D’
A
B C’ B’
F C
E D rotation none of these
Example: Drawing Transformations
Draw the image of the triangle after the
transformation.
A. Translation along AB so that
A’ coincides with B
A
B A’
C B’
C’
Example: Drawing Transformations
Draw the image of the triangle after the
transformation.
B. Reflection across BC.
A
B
B’
C
C’
A’
Example: Drawing Transformations
Draw the image of the triangle after the
transformation. C’
C. 90° clockwise
rotation around point B A’
A
B’
B
C
Try This
Draw the image of the polygon after the
transformation.
A. Translation along DE so that B’ C’
E’ coincides with D
A’ F’
B C D’
E’
A F D
E
Try This
Draw the image of the polygon after the
transformation.
B. Reflection across CD.
B B’
C C’
A F D D’ F’ A’
E E’
Try This
Draw the image of the polygon after the
transformation.
C. 90° counterclockwise
rotation around point C
B D’
C C’
B’
F’ E’
A F D
A’
E
Reflection and Translation
Dilation and Rotation
Example: Graphing
Transformations
Draw the image of a triangle with vertices of (1, 1),
(2, –2 ), and (5, 0) after each transformation.
A. 180° counterclockwise rotation around (0, 0)
Example: Graphing
Transformations
Draw the image of a triangle with vertices of (1, 1),
(2, –2 ), and (5, 0) after each transformation.
B. Translation 5 units left
Example: Graphing
Transformations
Draw the image of a triangle with vertices of (1, 1),
(2, –2 ), and (5, 0) after each transformation.
C. Reflection across the x-axis
Try This
Draw the image of a shape with vertices of (1, –2),
(3, 2), (7, 3), and (6, –1) after each transformation.
A. 180° clockwise rotation around (0, 0)
y
2
x
–2
Try This
Draw the image of a shape with vertices of (1, –2),
(3, 2), (7, 3), and (6, –1) after each transformation.
B. Translation 10 units left
y
2
x
–2
Try This
Draw the image of a shape with vertices of (1, –2),
(3, 2), (7, 3), and (6, –1) after each transformation.
C. Reflection across the x-axis
y
2
x
–2
Lesson Quiz: Part 1
Given the coordinates for the vertices of
each pair of quadrilaterals, determine
whether each pair represents a translation,
rotation, reflection, or none of these.
1. (2, 2), (4, 0), (3, 5), (6, 4)
and translation
(3, –1), (5, –3), (4, 2), (7, 1)
2. (2, 3), (5, 5), (1, –2), (5, –4)
and reflection
(–2, 3), (–5, 5), (–1, –2), (–5, –4)
Lesson Quiz: Part 2
Given the coordinates for the vertices of
each pair of quadrilaterals, determine
whether each pair represents a translation,
rotation, reflection, or none of these.
3. (1, 3), (–1, 2), (2, –3), (4, 0)
and none
(1, –3), (–1, 2), (–2, 3), (–4, 0)
4. (4, 1), (1, 2), (4, 5), (1, 5)
and rotation
(–4, –1), (–1, –2), (–4, –5), (–1, –5)