Deer Valley Unified School District
8th Grade Math
Unit 2
Pre-Test should take 15 minutes or less
Name ___________________________________
Date ____________________________________
Approved for use on test: Graph paper
SECTION I: PREREQUISITE UNIT KNOWLEDGE (Pre-Test)
1) Which transformation creates
an image that is not the same size
as the original?
2) Identify the following
transformation.
Use the coordinate plane below to answer the following
questions.
B
A
3) The images below shows what
type of transformation?
6) Graph and label the following points on the
coordinate plane
X) (3, -5)
Y) (-2, 6)
Z) (0, 2)
7) Label each of the 4 quadrants on the coordinate
plane to the left.
8) Identify the coordinates of the following points.
a) Point A ______________
b) Point B ______________
Section 2 Unit Knowledge (Pre-Test)
4) Triangle ABC has undergone a series of transformations to result in figure B;
where q, r, and s represent the lengths of the sides in Figure B. Determine which
sides of the triangles are congruent.
A
5) Is Figure A congruent to Figure
B? Explain how you know.
B
C
Q
Figure B
R
S
___________________________
___________________________
AB  ___________
BC  ___________
AC  ___________
___________________________
___________________________
Deer Valley Unified School District
8th Grade Math
Unit 2
6) Triangle ABC is shown in the
coordinate plane below. Rotate
triangle ABC 270 degrees
counterclockwise about the origin and
then translate it 6 units left. Label the
resulting image XYZ and identify the
vertices of the image.
Name ___________________________________
Date ____________________________________
7) A figure is rotated 180o about the
origin then it is reflected. Is the image
congruent to the original figure?
Explain your reasoning.
________________________________
A
________________________________
B
C
________________________________
________________________________
________________________________
________________________________
X ___________
Y ___________
Z ___________
Deer Valley Unified School District
8th Grade Math
Unit 2
Name ___________________________________
Date ____________________________________
RUBRIC for “WRITING TO EXPLAIN” Questions:
3 points
Student shows a clear
understanding of concept by
using written explanation
and/or visual models to solve
the problem correctly.
2 points
Student shows some understanding
of concept by using written
explanation and/or visual models
to solve the problem.
(minor error in understanding)
1 point
Student shows little
understanding of concept.
Student may have correct answer,
but no evidence of understanding,
or incorrect answer but little
evidence of understanding is
present.
Unit 2 Post-Test
Approved for use on test: Graph paper
Write to explain (3 points)
1) ABC is rotated 180o about the
*2) Is Figure A congruent to Figure
origin to form DEF. Rotate the
A’? Explain how you know.
image and identify the vertices of
the image.
0 points
Student writes incorrect
answer and shows no
evidence of understanding.
3) Find the coordinates of triangle
ABC with vertices of A (4, 5), B (5,1),
C (2,3) after a reflection across the
y-axis.
A) A’ (4, 5), B’ (5, 1), C’ (2, 3)
B) A’ (-4, -5), B’ (-5, -1), C’ (-2, -3)
C) A’ (4, -5), B’ (5, -1), C’ (2, -3)
_____________________________
D) A’ (-4, 5), B’ (-5, 1), C’ (-2, 3)
_____________________________
_____________________________
_____________________________
D ______ E _______ F _______
_____________________________
4) Describe a sequence of transformations that can be used to show that triangle ABC is congruent to triangle
XYZ.
A) Triangle ABC is rotated 180o about the origin.
X
Y
B) Triangle ABC is reflected over the y-axis then translated 7
units up.
Z
C) Triangle ABC is reflected over the x-axis, then rotated 90o
clockwise about the origin.
B
C
D) Triangle ABC is translated 10 units right and 10 units up.
A
Y
Z
X
Deer Valley Unified School District
8th Grade Math
Unit 2
Write to explain (3 points)
5) Describe the sequence of
transformations that results in the
transformation of figure A to figure
A’. Be detailed in your description.
Name ___________________________________
Date ____________________________________
*6) Triangle ABC was reflected over
the x-axis and then reflected over the
y-axis to form its image, where x, y,
and z represent the lengths of the
sides Figure B. Determine which sides
of the triangles are congruent.
*7) Parallelogram EFGH is shown in
the coordinate plane below. Rotate
EFGH 90 degrees clockwise about the
origin and then translate it 3 units
down. Label the resulting image
PQRS and identify the vertices of the
image.
Figure A
______________________________
______________________________
Figure B
______________________________
______________________________
______________________________
AB  ___________
BC  ___________
AC  ___________
P _________
Q _________
R _________
S _________
8) Triangle ABC is shown below on the coordinate plane. Triangle XYZ (not shown) has coordinates X (5, -2),
Y (2, -2), Z (2, -5). Which of the following statement(s) is TRUE about triangle ABC and triangle XYZ?
SELECT ALL THAT APPLY.
A
B
A.
ABC 
XYZ since it is reflected over the x-axis and is
B.
ABC 
XYZ since it is reflected over the y-axis and is not
C.
ABC 
XYZ.
XYZ since
D.
ABC 
XYZ since ABC is rotated 90o counter clockwise about the
origin and is not XYZ.
E.
ABC  XYZ since
origin and is XYZ.
C
XYZ.
XYZ.
ABC is rotated 90o clockwise about the origin and is
ABC is rotated counterclockwise 270o about the
Deer Valley Unified School District
8th Grade Math
Unit 2
Write to explain (3 points)
*9) A figure that is translated then
reflected on a coordinate plane is
always, sometimes, or never
congruent to its image? Defend and
prove your reasoning.
Name ___________________________________
Date ____________________________________
10) Which of the following
transformations will result in an
image that is congruent to the
original figure? SELECT ALL THAT
APPLY.
A) Dilation
_______________________________
_______________________________
B) Reflection
_______________________________
C) Translation
_______________________________
_______________________________
_______________________________
* Denotes pre/post test questions.
D) Rotation
Deer Valley Unified School District
8th Grade Math
Unit 2
Name ___________________________________
Date ____________________________________
ANSWER KEY
Pre-Test should take 15
SECTION I: PREREQUISITE UNIT KNOWLEDGE (Pre-Test)
1) Which transformation creates
an image that is not the same size
as the original?
Answer: Dilation
2) Identify the following
transformation.
3) The images below shows what
type of transformation?
Answer: Rotation
Answer: Translation
Use the coordinate plane below to answer the following
questions.
Quadrant I
Y
Quadrant 2
A
6) Graph and label the following points on the
coordinate plane
X) (3, -5)
Y) (-2, 6)
Z) (0, 2)
B
Z
7) Label each of the 4 quadrants on the coordinate
plane to the left.
8) Identify the coordinates of the following points.
X
Quadrant 3
Quadrant 4
(-6, 3)
a) Point A ______________
(8, 2)
b) Point B ______________
Section 2 Unit Knowledge (Pre-Test)
4) Triangle ABC has undergone a series of transformations to result in figure B;
where q, r, and s represent the lengths of the sides in Figure B. Determine which
sides of the triangles are congruent.
A
5) Is Figure A congruent to figure
B? Explain how you know.
B
C
Q
Figure B
R
S
R
AB  ___________
S
BC  ___________
AC  ___________
Q
Yes, because figure B has
undergone a transformation which
results in the image changing
location and orientation but not
size. Therefore, figure A is
congruent to figure B
Deer Valley Unified School District
8th Grade Math
Unit 2
6) Triangle ABC is shown in the
coordinate plane below. Rotate
triangle ABC 270 degrees
counterclockwise about the origin and
then translate it 6 units left. Label the
resulting image XYZ and identify the
vertices of the image.
A
B
Y
X
Z
(-1, -2)
X ___________
(-4, -2)
Y ___________
(-4, -5)
Z ___________
C
Name ___________________________________
Date ____________________________________
7) A figure is rotated 180o about the
origin then it is reflected. Is the image
congruent to the original figure?
Explain your reasoning.
Yes, because any time you rotate
and/or reflect a figure the size
doesn’t change, but the location
and the orientation will.
Therefore, the image will be
congruent to the original.
Deer Valley Unified School District
8th Grade Math
Unit 2
Name ___________________________________
Date ____________________________________
RUBRIC for “WRITING TO EXPLAIN” Questions:
3 points
Student shows a clear
understanding of concept by
using written explanation
and/or visual models to solve
the problem correctly.
2 points
Student shows some understanding
of concept by using written
explanation and/or visual models
to solve the problem.
(minor error in understanding)
1 point
Student shows little
understanding of concept.
Student may have correct answer,
but no evidence of understanding,
or incorrect answer but little
evidence of understanding is
present.
0 points
Student writes incorrect
answer and shows no
evidence of understanding.
ANSWER KEY
Unit 2 Post-Test
Approve for use on test: Graph paper
Write to explain (3 points)
1) ABC is rotated 180o about the
*2) Is Figure A congruent to Figure
origin to form DEF. Rotate the
A’? Explain how you know.
image and identify the vertices of
the image.
3) Find the coordinates of triangle
ABC with vertices of A (4, 5), B (5,1),
C (2,3) after a reflection across the
y-axis.
A. A’ (4, 5), B’ (5, 1), C’ (2, 3)
B. A’ (-4, -5), B’ (-5, -1), C’ (-2, -3)
Yes, because figure A is congruent
to figure A’ because figure A has
undergone a translation which
changed its location but not its size
or orientation. Therefore, the
image will be congruent to the
original.
(4, 2) F _______
(7, 4) E _______
(3, 8)
D ______
C. A’ (4, -5), B’ (5, -1), C’ (2, -3)
D. A’ (-4, 5), B’ (-5, 1), C’ (-2, 3)
4) Describe a sequence of transformations that can be used to show that triangle ABC is congruent to triangle
XYZ.
A) Triangle ABC is rotated 180o about the origin.
X
Y
B) Triangle ABC is reflected over the y-axis then translated 7
units up.
Z
C) Triangle ABC is reflected over the x-axis, then rotated 90o
clockwise about the origin.
B
C
D) Triangle ABC is translated 10 units right and 10 units up.
A
Y
Z
X
Deer Valley Unified School District
8th Grade Math
Unit 2
Write to explain (3 points)
5) Describe the sequence of
transformations that results in the
transformation of figure A to figure
A’. Be detailed in your description.
Name ___________________________________
Date ____________________________________
*6) Triangle ABC was reflected over
the x-axis and then reflected over the
y-axis to form its image, where x, y,
and z represent the lengths of the
sides Figure B. Determine which sides
of the triangles are congruent.
*7) Parallelogram EFGH is shown in
the coordinate plane below. Rotate
EFGH 90 degrees clockwise about the
origin and then translate it 3 units
down. Label the resulting image
PQRS and identify the vertices of the
image.
Figure A
Yes, because figure A is
congruent to figure A’ because
figure A has undergone a 90o
clockwise rotation about the
origin which changed its location
but not its size or orientation.
Therefore, the image will be
congruent to the original.
Figure B
Z
AB  ___________
Y
BC  ___________
X
AC  ___________
(1, -4)
P _________
(5, -5)
Q _________
(5, -7)
R _________
(1, -6)
S _________
8) Triangle ABC is shown below on the coordinate plane. Triangle XYZ (not shown) has coordinates X (5, -2),
Y (2, -2), Z (2, -5). Which of the following statement(s) is TRUE about triangle ABC and triangle XYZ?
SELECT ALL THAT APPLY.
A
B
A.
ABC 
XYZ since it is reflected over the x-axis and is
B.
ABC 
XYZ since it is reflected over the y-axis and is not
C.
ABC 
XYZ.
XYZ since
D.
ABC 
XYZ since ABC is rotated 90o counter clockwise about the
origin and is not XYZ.
E.
ABC  XYZ since
origin and is XYZ.
C
XYZ.
XYZ.
ABC is rotated 90o clockwise about the origin and is
ABC is rotated counterclockwise 270o about the
Deer Valley Unified School District
8th Grade Math
Unit 2
Write to explain (3 points)
*9) A figure that is translated then
reflected on a coordinate plane is
always, sometimes, or never
congruent to its image? Defend and
prove your reasoning.
Always congruent because any
time you translate and/or reflect a
figure the size doesn’t change, but
the location and the orientation
will. Therefore, the image will be
congruent to the original.
Name ___________________________________
Date ____________________________________
10) Which of the following
transformations will result in an
image that is congruent to the
original figure? SELECT ALL THAT
APPLY.
A. Dilation
B. Reflection
C. Translation
D. Rotation
* Denotes pre/post test questions.