# Geometry Semester 1 review packet 2011-12

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```					Geometry: Semester Exam Review                                              Name: ___________________________
January 23                        January 24                     January 25                      January 26
SEMESTER FINAL Exams:              SEMESTER FINAL Exams:             SEMESTER FINAL Exams:         SEMESTER FINAL Exams:
Period 4:     8:00am – 9:50 am     Period 8:     8:00am – 9:50 am    Per 1:     8:00am – 9:50 am   Per 5:     8:00am – 9:50 am
Period 2 & A: 10:05 – 11:55 am     Period 7 & C: 10:05 – 11:55 am    Per 3 & D: 10:05 – 11:55 am   Per 6 & B: 10:05 – 11:55 am

During exam week, you will be expected to display a cumulative understanding of the concepts discussed in class during the first 20
weeks. This review packet was created to help you prepare for the exam and given to you several weeks in advance to help prevent
becoming too overwhelmed with the amount of review. Over the winter vacation, continue to study and work through the practice
problems. Completion of this packet is voluntary and answer keys will be made available when you are ready. Remember the exam
will be worth 10%(one letter grade) of your overall grade in class. Exam review sessions will replace POW review in January.

Find each sum or difference.
6        36       3                 1   3  0        5  0     5              9   7     8  10 5 2
              
1.
7
          7
2          2

2.
4
    0 1
           2  1
 

2
3.   6   3
       
4 4 1 9 
              

Given the following Matrices find either the sum or difference
        1          
1             4   5                  1 2                     3  44               2 4 7            11 
D                    2
2                                                                                  8
A                                 B  0.33 4               C  1 0     
2                                                                                      3 2 1            10 
9
3                             7   0.15                14  23.3
8                                                                                      11 

        5          


4. A + D                  5. D – A                  6. B – C                   7. A + B + C                  8.   A + ( C- D)

Find the dimensions of each product matrix. Then find the product, if possible. If the product is not defined explain why not.
 2 4 2                          1.0  80 
1 0 5                                                                              9 6 3 0   4 2
9.               0 10 4                     10.  0.25   42                      11.                      
0.5  91                                                         
2 1 6 0 1 7                                                                   1 6 3 9  2 4

12. The upcoming LMSA play will yield a nice profit for the Drama Department based on ticket prices and sales. Provide the
following ticket sales and prices write a matrix that represents the income from the play each day.

Ticket Prices by Location                                            Number of Tickets Sold
Location          Thursday             Friday           Saturday
Orchestra         Main         Balcony
Orchestra         150                  130              160
Ticket          \$7.00             \$6.00        \$5.00
Price                                                            Main              125                  130              175
Balcony           60                   52               80

13. Describe the necessary qualifications in order to multiply two matrices.

14. Describe the identity and inverse properties of matrices. Give an example of each.

15.
16. A youth group with 26 members is going on an overnight camping trip. Each of the 5 chaperones will drive a van or sedan. The
vans can seat 7 people, and the sedans can seat 5 people. How many of each type vehicle could transport everyone to the camping
area in one trip?
a. Write a systems of equations for the problem
b. Use linear combination to solve the systems.
c. Graph the two equations.

17. The internet is an electronic network where people share information and opinions. The chart below shows what two companies
charge for internet access.

Base Rate                    Hourly Rate
AT & Me                     \$9.95                         \$2.25
ComSassy                    No Base Fee                   \$2.95

a.   Write a system of equations to represent the cost c for t hours of access in one month from each company.
b.   For how many hours of use will both companies charge the same amount?
c.   If you used the internet about 20 hours per month, which company would you choose? Why?

18. Write the equation in standard form: y – 2 = ½(x-6)

19. What is the equation of the line perpendicular to the line with undefined slope passing through the point (6, -3)?

20. What is the equation of the line perpendicular to the line with undefined slope passing through the point (7, 0)?

21. What is the equation of the line passing through the point (7, -4) and parallel to the equation x = 10?

22. What is the equation of the line passing through the point (-2, 4) and parallel to the equation y = 7?

23. Given the following coordinates (6, 7) and (4,-8).
a. Graph the coordinates on graph paper.
b. Find the equation of the line which contains these two points.
c. Determine the length of the segment created by these two points.
4
d.   Determine if the line is parallel, perpendicular or neither to the line y =       x +3.
5

24. A quadrilateral has vertices at (2,1), ( 7,1), (5,9) and (4,9).
a. What type of quadrilateral is this?
b. Find the midpoints of the sides that aren’t parallel.

25. Quadrilateral STAY has vertices S(-1,1), T(7,6), A(3,3) and Y(-3,-4).
a. What type of quadrilateral is STAY?
b. How long is diagonal SA?
c. At what point do the two diagonals intersect?

26. Triangle ABC is enclosed by three lines as shown here.

a.   Write equations for the sides of ΔABC.
b.   For each equation, what restrictions on the input values for x and y
confine the lines to the sides of the triangle? (write inequality
boundaries)
c.   Is ΔABC a special kind of triangle? Explain your reasoning.
d.   Find the area of ΔABC
.
27. The three lines 4x – 3y = 0, 2x – 5y = 0, and x + y = 7 determine a triangle

a.   Find the coordinates of the vertices.
b.   Each segment perpendicular to a side from the vertex opposite that side is called
an altitude of the triangle. Write equations of the lines containing the altitudes
for this triangle.

28. What is the area of the shaded region of the figure at the right?

Solve.
1                1                2              7 x 1        19 x 3                  3x  9       2x  6
29.          ( y  1)        ( y  3)        30.   2           3x                     31.            
4                6                3                6              4                       6            4

32. A line described by the equation y = 5x – 7. Points (x, y) that solve the equation must lie on the line. Which of the points
(3, 8), (-2, -17), (0, -7), (4, 11), and (1, -2) are on the line?

33. Suppose quadrilateral PQRS contains the vertices P(-10, 7), Q(4, 3), R(-2, -5), S(-16, 1).
a) Show that quadrilateral PQRS is not a parallelogram.
b) Show that the quadrilateral formed by joining consecutive midpoints of the sides of PQRS is a parallelogram.

34. Give the most descriptive name for
a. A quadrilateral with diagonals that are perpendicular bisectors of each other.
b. A rectangle that is also a kite.
c. A quadrilateral with opposite angles supplementary and consecutive angles supplementary.
d. A quadrilateral with one pair of opposite sides congruent and the other pair of opposite sides parallel.

35.   What is the most descriptive name for a quadrilateral with vertices (-7, 2), (2, 8), (6, 2), and (-3, -4)? Justify your conclusion.

36.   If a quadrilateral is symmetrical across both diagonals, it is a _____________.

37.   If a quadrilateral is symmetrical across exactly one diagonal, it is a ________.

38.   Which quadrilateral has four axes of symmetry? _________

39.   Suppose SQUA has vertices S(3, 3), Q(3, 10), U(10, 10), and A(10, 3). What is the most descriptive name for the quadrilaterals
SQUA and Q’QAA’, where Q’ is the reflection of Q over the y-axis and A’ is the reflection of A over the x-axis? Justify your
conclusions.

40. What is the name for the quadrilateral with vertices (3, 2), (8, 1), (7, 6), and (2, 7). Justify your conclusion.

41.   Find the image of ΔABC with vertices A(3,1), B(-2,0) and C(1,5) under each transformation.
a. translation left 5, up 2
b. dilation of size 5
c. translation 2, down 4
42. Suppose    JOE contains the vertices J(-6, -4), O(3, 2), and E(-2, 5). Sketch and label    J ' O' E ' under the following conditions.
a. Translate JOE according to the rule ( x, y)  ( x  4, y  2) .
b. Reflect JOE over the y-axis.
c. Reflect JOE over the line y = -x.
d. Rotate JOE counterclockwise 270°.

44. Given the points (7, -3) and (-6, -10), calculate the distance between the two points, the slope of the line that connects these two
points, and the midpoint of the segment that joins these two points.

45. Write the standard form of an equation of the line that passes through the given point and has the given slope:
4                                               8                                       1
a. (12, -7), m =                            b. (-3, -6), m =                            c. (0, -9), m =
5                                               3                                       7
46. Write the standard form of an equation of the line that passes through each pair of points:
a. (10, 9), (-3, 5)                            b. (-6, -3), (-8, -11)                   c.(-12, 2), (-8, -4)

47. i.) Calculate the x-intercept and y-intercept for the following lines and ii) write each in slope intercept form.
a. -7x + 2y = 14                   b. x – 3y = 12               c. 5x + 6y = 13             d. -2x – 8y = 18

48. Solve the following systems using any method (substitution, elimination, graphing, or matrix):
x  y  12                                       2 x  5y  9                              3x  2 y  12
a.)                                              b.)                                       c.)
7x  2 y  3                                     4 x  8 y  18                            6 x  4 y  15

49. Simplify (give exact answers only):
a.)    56x 2 y 3
b.)    84  525

c.) 7 3  ( 2 3 )
d.) 2( 3 12 )  4( 2 27 )
12
e.)
3
50. Solve the following literal equations for the indicated variable:
1
a.)   A   h(b1  b2 ) for b1
2
b.) E  mc for c
2

c.) y  y1  m( x  x1 ) for m

51. Find the equation of the line that contains the point (-7, -3) and is parallel to the line with equation -6x – 3y = 12.

52. Find the equation of the line that contains the point (6, -2) and is perpendicular to the line with equation y = 4x – 8.
53. Find the area of the figure at the below.                                  54. Find the shaded area in the figure below.

55. Represent the inventory data at the right in matrix, M. (Be sure to title and label the matrix.) Explain what the entry in the third
row, second column means.

Inventory
Items                   Small   Medium       Large
Jerseys                 12      28           17
T-shirts                15      32           45
Sweatshirts             6       20           30

56. A financial manager wants to invest \$50,000 for a client by putting some of the money in a low-risk investment that earns 5% per
year and some of the money in a high-risk investment that earns 14% per year. Set up a system of equations and then solve this
system with matrices to determine how much money should be invested at each interest rate to earn \$5,000 in interest per year.

57. The following digraph represents an instance of social dominance amongst five people. An arrow illustrates the direction of
dominance. For example, Person B dominates Person C.

Social Dominance Digraph for Five People
a.     Construct an adjacency matrix, A, for the above digraph.
B
b.     Calculate A². What does the A² matrix represent in this situation?
c.     Rank the social dominance in order from most dominant to least dominant.
d.
_______        ________          ________          ________           _______
A                                                  C

D
E

58. If a rectangle measures 54 meters by 72 meters, what is the length, in meters, of the diagonal of the rectangle?

59. If the system of equations y = 2x – 5 and -3y = kx – 2 has no solutions, what is the value of k?

60. The midpoint of the line segment AC in the standard (x, y) coordinate plane has coordinates (4, 8). The (x, y) coordinates of A
and C are (4, 2) and (4, s), respectively. What is the value of s?

Find the measure of the following angles then classify each as acute,
C                                       right, straight or obtuse using the figure at the left:
61) m BDF = _______ ____________________
62) m 1 = __________ ____________________
A                                       E
1                                           63) m BDC = _______ ____________________
64) m 2 = __________ ____________________
2                  48°
50º
65) m ADE = ______ ____________________
D
B                    3          F
66) Use the figure above to find: a) Two angles that are complementary b) Two angles forming a linear pair c) Two vertical angles
____________________________          _________________________           _______________
67)

a) Use the rectangle at the left to find the value of a. ___________
6a               3(a + 12)
b) Find the width of the rectangle if the perimeter is 200 units. __________

5x  4
68) Solve:      4x + 2(3x – 8) =               ___________
3

69) Find the value of x, y and z and measures of all missing angles in the figure below. l         m, a     b

6z                  x = _______       y = ________ z = ________

(4y +22)             (9x+6) 
m2 = _____ m5=____ m6= _____
(6x-6) 
m13= _____ m9= ____ m11= ____

70. What is the name of the angle relationship for angles 3 & 9 above? 1 & 6? 2 & 8? 2 & 7?

71.    RST is isosceles with S as the vertex angle. SR = 10x + 8, ST = 6(x + 12), RT = 10x - 5 Find the length of the base.

72. Solve the following system of equations with all four methods: graphing, substitution, elimination (combinations), and matrices.
2x – 2y = -80
6x – y = 100

Simplify.
45                          64
73.     48     ___________           74.     98x 4    __________             75.         _________ 76.                    __________
100                           7

77. Find the distance and midpoint between the two points given. Simplify all radical answers

(-2, -4) (3, 8)_______                          (-3, -5) (2, 5)________

8 28 24 4 
78. Given the quadrilateral QUAD with vertex matrix          QUAD =     4 12 28 20 use the length of each side and their slopes
          
to determine the type of quadrilateral. Explain.

79. On graph paper, sketch triangle ABC on three separate coordinate grids. A (-1,2) B (2,5) C (2,2)
a) sketch and label a reflection across the y-axis
b) sketch and label a reflection across the line y = x
c) sketch and label a translation with components -3 and 2
d) rotation of 90 degrees counterclockwise about the origin

80. A size transformation with magnitude 3.5 and center at the origin transforms a right triangle with legs of 4 cm and 5 cm.
a) What are the lengths of the three sides of the image triangle? b) What are the areas of the given triangle and of its image?

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