8th Grade Benchmark 4
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Which transformation has been applied?
y
10
8
6
4
2
–10 –8
–6
–4
–2
–2
2
4
6
8
10
x
–4
–6
–8
–10
a. Rotation
b. Dilation
____
c. Reflection
d. Translation
2. The following picture shows which transformation?
y
10
8
6
4
2
–10 –8
–6
–4
–2
–2
2
4
6
8
10
x
–4
–6
–8
–10
a. Rotation with center at the origin
b. Reflection over the y-axis
c. Reflection over the x-axis
d. Translation down
____
3. Rectangle PQRS is shown on the graph. If rectangle PQRS is rotated 180 degrees clockwise about the origin,
what are the new coordinates of point P?
y
10
8
6
4
P
Q
S
R
2
–10 –8
–6
–4
–2
–2
2
4
6
8
10
x
–4
–6
–8
–10
a. (-2, -4)
b. (2, -4)
____
c. (-4, -2)
d. (4, -2)
4. Quadrilateral ABCD is shown on this graph. If Quadrilateral ABCD is rotated 90º clockwise about the origin,
what are the new coordinates of point D?
y
10
8
6
A
B
4
2
–10 –8
–6
–4
–2
–2
D
C
2
4
6
8
10
x
–4
–6
–8
–10
a. (2, 3)
b. (-3, -2)
c. (-3, 2)
d. (3, -2)
____
5. What sequence of events transforms triangle ABC to triangle A’B’C’
y
10
8
6
C
4
2
B
–10 –8
A
–6
–4
–2
–2
2
4
6
8
A'
–4
10
x
C'
–6
–8
B'
–10
a. Reflect over x-axis; rotate 90º clockwise
around the origin; translate 4 units to the
right.
b. Reflect over y-axis; rotate 90º
counterclockwise around the origin;
translate 4 units to the right.
____
6. Given a triangle with the vertices at (-1, 3), (4, 3) and (0,1); find the new vertices of the triangle after undergoing
the transformation described by the rule below.
a. (3, -1), (3, 4) and (0, 1)
b. (-3, 8), (2, 8) and (-2, 6)
____
c. Reflect over y-axis; rotate 90º clockwise
around the origin; translate 4 units to the
right.
d. Reflect over y-axis; rotate 90º clockwise
around the origin; translate 4 units to the
left.
c. (1, -3), (-4, -3) and (0, -1)
d. (4, 1), (9, 1) and (5, -1)
7. Given the original shape V and its image V’ on a coordinate plane, determine the transformation rule or rules
that translated the original or pre-image to the resulting image.
y
10
8
6
4
V
–10 –8
–6
V'
2
–4
–2
–2
2
4
6
8
10
x
–4
–6
–8
–10
a.
c.
b.
d.
____
8. Which transformation has been applied?
y
10
8
6
4
2
–10 –8
–6
X'
–4
–2
–2
X
–4
2
4
6
8
10
x
–6
–8
–10
a. Rotation
b. Dilation
____
c. Reflection
d. Translation
9. Which of the following transformation rules will not result in a similar figure?
a.
c.
b.
d.
____ 10. Given the orignal shape V and it’s image V’ list the sequence of transformations that verifies the similarity of
the two figures.
a.
Dilate by a scale factor of
; rotation of
c. Dilate by a scale factor of 2; rotation of
90º clockwise about the origin
90º clockwise about the origin
b.
Dilate by a scale factor of
; rotation of
90º counter-clockwise about the origin
d. Dilate by a scale factor of 2; rotation of
90º counter-clockwise about the origin
____ 11. Describe the sequence of transformations given by the transformation rule;
and graph
below.
a. Reflect over the y-axis; dilate by a scale
factor of 2.
b. Rotate 90º counter-clockwise; dilate by a
scale factor of 2
____ 12. In the diagram below
a. 63º
b. 117º
c. Reflect over the x-axis; dilate by a scale
factor of 2.
d. Translate up 1; reflect over the x-axis.
and the measurement of angle 1 = 117. Find the
c. 54º
d. 180º
.
____ 13. What is the measure of angle 1 on the roof in the picture below?
a. 89º
b. 86º
c. 136º
d. 183º
____ 14. Are the two triangles similar, why or why not?
a. Yes; using the triangle sum theorem you c. No; the angles are not proportional
can find the measure of the missing angle
for each triangle. Upon doing so, two sets
of cooresponding angles are congruent so
the triangles are ximilar by AA similarity.
b. No; the triangles are not congruent because d. There is not enough information to
the corresponding angles are not congruent
determine if they are similar.
so AA similarity does not work
____ 15. Given:
a. 85º
b. 90º
. What is the
?
c. 95º
d. 100º
____ 16. What is the relationship between angle 1 and angle 5?
a. opposite interior angles
b. corresponding angles
____ 17. Given
a. 65º
b. 25º
c. consecutive interior angles
d. alternate exterior angles
. What is the
c. 125º
d. 115º
____ 18. Suppose you have a triangle with side lengths 7, 24, 25. Is it a right triangle?
a. Yes, it is a right triangle
c. No, it is an obtuse triangle
b. No, it is an isosceles triangle
d. Not enough information to tell
____ 19. Using the illustration below, what is the aproximate height of the hot air balloon.
a. 954 feet
b. 1,192feet
c. 1,202 feet
d. 1,498 feet
____ 20. A spider has taken up residence in a small cardboard box which measures 2 inches by 4 inches by 4 inches.
What is the length, in inches, of a straight spider web that will carry the spider from the lower right front corner
of the box to the upper left back corner of the box?
a. 4.47 in.
b. 5.66 in.
c. 5 in.
d. 6 in.
____ 21. Use the Pythagorean Theorem to find the distance between (1, 4) and (4, 0).
a. 25 units
c. 16 units
b. 5 units
d. 4 units
____ 22. A cylindrical silo has 1600
radius of the silo?
a. 6.03 ft
b. 10.1 ft
of grain. The grain fills the silo to a 25ft. in height. What is the approximate
c. 209 ft
d. 4.51 ft
____ 23. Below is a picture of a perfectly spherical scoop of ice cream. If you eat two of these scoops how much ice
cream will you have consumed. Round your answer to the nearest tenth.
a. 18.8
b. 14.13
c. 28.3
d. 30.1
____ 24. Which will hold the most water: two cones, one with a 3 cm radius and the other with a 4 cm radius, or a cone
with a 5 cm radius?(Assume all the hieghts are the same)
a. The two cones will hold more water
c. They both hold the same amount of water.
b. The 5 cm radius cone will hold more water d. There is not enough information to know.
Short Answer
25. Given
in the graph below, explain how you know they are congruent and similar.
26.Given the parallel lines with a transversal below and
Answer the following questions for each.
Angle Size
Angle relationship which helped you figure out the angle size.
(words to use: equal, supplemental, vertical, alternate interior, corresponding, alternate
consecitive interior)
a.
b.
c.
d.
e.
f.
27.The opposite sides of a quadrilateral are congruent. The sides measure 9 in. and 40 in. and
the diagonal measures 41 in.
a) Draw and label a picture of this quadrilateral
b) Is the quadrilateral a rectangle? Explain your answer
exterior,
28.For each of the following problems draw and label a picture to help you answer each question.
a) A little kid has an ice cream cone (one scoop). It’s a hot day outside, and the ice cream starts to melt. The
radius of the cone and the ice cream (sphere) is 4 cm and the height of the cone is 8 cm. Will all of the melted ice
cream fit inside the cone? Explain and justify your response.
b) A cylindrical glass 7 cm in diameter and 10 cm tall is filled with water to a height of 8 cm. If a ball 5 cm in
diameter is dropped into the glass and sinks to the bottom, will the water in the glass overflow? Explain and
justify your response.
8th Grade Benchmark 4
Answer Section
MULTIPLE CHOICE
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
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20.
21.
22.
23.
24.
ANS:
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TOP:
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ANS:
D
PTS: 1
STA: 8.G.1
C
PTS: 1
STA: 8.G.1&2
A
PTS: 1
STA: 8.G.1&3
D
PTS: 1
STA: 8.G.1&3
C
PTS: 1
STA: 8.G.2
D
PTS: 1
STA: 8.G.3
C
PTS: 1
STA: 8.G.3
B
PTS: 1
STA: 8.G.4
C
PTS: 1
STA: 8.G.4
Similarity Transformations using coordinates
B
PTS: 1
STA: 8.G.2&4
Combinations of similarity transformations
C
PTS: 1
STA: 8.G.2&4
Combinations of similarity transformations
C
PTS: 1
STA: 8.G.5
Exterior Angle and Angle Sum Theorem
A
PTS: 1
STA: 8.G.5
Exterior Angle and Angle Sum Theorem
A
PTS: 1
STA: 8.G.5
A
PTS: 1
STA: 8.G.5
B
PTS: 1
STA: 8.G.5
D
PTS: 1
STA: 8.G.5
A
PTS: 1
STA: 8.G.6
D
PTS: 1
STA: 8.G.7
Pythagorean Theorem in real-world applications
D
PTS: 1
STA: 8.G.7
Pythagorean Theorem in real-world applications
B
PTS: 1
STA: 8.G.8
Pythagorean Theorem in the coordinate system
D
PTS: 1
STA: 8.G.9
C
PTS: 1
STA: 8.G.9
C
PTS: 1
STA: 8.G.9
SHORT ANSWER
25. ANS:
TOP:
TOP:
TOP:
TOP:
TOP:
TOP:
TOP:
TOP:
Properties of Transformations
Properties of Transformations
Transformations using coordinates
Transformations using coordinates
Combination of transformations
Transformations using coordinates
Transformations using coordinates
Similarity Transformations
TOP:
TOP:
TOP:
TOP:
TOP:
AA similarity
Parallel lines and transversals
Parallel lines and transversals
Parallel lines and transversals
Pythagorean Theorem
TOP: Volume of a cylinder
TOP: Volume of a sphere
TOP: Volume of a cone
PTS: 1
26. ANS:
PTS: 1
27. ANS:
PTS: 1
28. ANS:
PTS: 1