Unit: Transformational Geometry
Name ____________________________
Assessment Review
Period ___________ Date ____________
G.CO.2 Learning Target: I can describe a
transformation using coordinate notation that maps
one point onto a unique image point. I can compare
transformations that preserve distance and angle to
those that do not.
1. Translate the quadrilateral
,
,
3. ∆JKL is rotated 90° clockwise about the origin
and then translated using
.
What are the coordinates of the final image of
point L under this composition of
transformations?
,
using the transformation
( x, y )  ( x  2, y  3) .
A.
B.
,
,
C.
D.
,
,
,
,
,
,
,
,
,
,
Answer:_____________________________
2. After a translation, the image
is
. Identify the image of the point Q
after this same translation. Then,
describe the rule of the rigid transformation in
coordinate notation and in words.
4. ∆ABC is translated using ( x, y )  ( x  1, y  3)
after it is reflected across the y-axis. What are the
coordinates of the final image of point C under this
composition of transformations?
y
Point Q’:__________________
4
Coordinate notation:
2
A
______________________________________
Words:
–4
–2
B
2
x
4
–2
______________________________________
C
–4
Answer:_____________________________
5. A triangle with vertices
,
, and
is rotated 180 degrees clockwise about
the point (-2, 1). Graph and label the pre-image
and the image.
G-CO.3: I can demonstrate the rotations and
reflections that carry a rectangle, parallelogram,
trapezoid, or regular polygon onto itself.
7. Complete the given chart given that you are
referencing REGULAR polygons:
Sides
Lines of
Symmetry
Degrees of
Rotational
Symmetry
3
4
5
6
7
Answer:_____________________________
8
6. What are the endpoints of the image
is reflected about the line
?
if
n
8. What rotation will map the figure onto
itself?
A.
B.
C.
D.
A.
B.
C.
D.
about the center
about the center
about the center
from the top
9. What is the angle of rotation that maps the
equilateral triangle onto itself?
11. Marta is studying the symmetry of a regular
pentagon drawn on a piece of paper.
C
B
A
Describe all the ways you can map A onto B?
Marta tried folding the paper along a vertical line
and horizontal line as shown below and
concluded that a regular pentagon has only 1 line
of symmetry.
Fold
Fold
10. Sketch a hexagon that has a line of
symmetry at y = -x + 5 below:
She then turned the paper upside down and noted
that the figure no longer looks the same. She
concluded a regular pentagon has no rotational
symmetry.
A. Explain the flaws in Marta’s reasoning
and describe the true symmetry of the
figure.
_________________________________
_________________________________
B. What is the smallest angle of rotation
that the figure maps onto itself?
_________________________________
G-CO.4: I can develop definitions of rotations,
reflections, and translations in terms of angles,
circles, perpendicular lines, parallel lines, and line
segments.
12. Identify a single transformation that is
equivalent to reflecting the figure across
line n and then reflecting that image across
line m.
15. Given the figure below.
Part A: Is
to
a congruence
transformation? Explain.
Answer:_____________________________
_________________________________
13. What angle of rotation maps
to
?
_________________________________
Part B: Is
to
a rotation? Explain.
_________________________________
_________________________________
Part C: Use coordinate notation to describe the
translation
to
.
A.
B.
C.
D.
14. . Which mapping represents a rotation of
clockwise about the origin?
A.
B.
C.
D.
_________________________________
_________________________________
16. Cassie claims the transformation rule
rotates figures 180 degrees
18. The vertices of
are
, and
about the origin. Plot
, the triangle
generated by this rule, and discuss whether
Cassie is correct.
. Find the
vertices of
after a composition of
the transformation in the order they are
listed.
y
Translation:
6
C
Reflection: in the -axis
5
4
3
2
1
–6 –5 –4 –3 –2 –1
–1
O
B
1
2
A
3
4
5
6
x
–2
–3
–4
–5
–6
Answer:
____________________________________
Answer:_____________________________
____________________________________
19. When
produce
___________________________________
17. If a point not on a given vertical line is
reflected over said line, then the point and
its image will ______________________.
a. be on the same vertical line.
b. be on the same horizontal line.
c. Both A and B
d. Neither A and B
is reflected over
to
, which statement will not necessarily
be true?
A.
B.
C.
D.
G-CO.6: I can decide if two shapes are congruent
because of the rigid motions between the two
figures. I can investigate rigid motions and
generalize their characteristics as preserving
congruence. I can find a sequence of
transformations that will carry a shape onto
another.
G-CO.5: I can demonstrate and draw
transformations. I can find a sequence of
transformations that will carry a shape onto
another
20.
with vertices
,
, and
is reflected across the y-axis, and then
its image is reflected across the line
.
P(–6, 1), Q(–5, 4), R(–2, 5), and S(–3, 2),
Which single transformation moves the triangle
from its starting position to its final position?
A.
B.
C.
D.
was reflected over the line x = –1.
Liam states that the reflection of PQRS must
also be a rhombus because a reflection is a
congruence transformation. Explain what Liam
means by this statement.
rotation by
about the origin
rotation by
about the origin
reflection across the x-axis
reflection across the y-axis
21. Ann wants to create a design to decorate her
Geometry binder. She reflects part of the design
across line p and then reflects the image across
line n. Describe a single transformation that
moves the part of the design from its starting
position to its final position.
p
Answer:
____________________________________
____________________________________
___________________________________
Start
n
Finish
A.
B.
C.
D.
22. Rhombus PQRS, with vertex coordinates
rotation of 180° about the origin
rotation of 90° about the origin
translation along the line
reflection across the line
23. Determine whether triangles
are congruent. Explain.
24. Suvi was given triangle ABC such that A(9, 1),
B (5, 3) and C (7, -4). He then was asked to
reflected it over the x-axis and translate it up 5
units. His answer was that the new coordinates of
the transformation would be A’’(9, 4), B’’(-5, 8)
and C’’(7, 9). After verifying by graphing his
answer he saw he was incorrect. What did Suvi do
incorrect, and correct his mistake.
and
y
6
G
–6
E
F
P
Q
6
R
–6
A. The triangles are congruent because
can be mapped to
by a
reflection:
.
B. The triangles are congruent because
can be mapped to
by a
rotation:
.
C. The triangles are congruent because
can be mapped to
by a
reflection:
.
D. The triangles are congruent because
can be mapped to
by a
rotation:
.
x