Geometry Review – Chapter 9 Transformations
Name:
**SHOW YOUR WORK**
Date:
Block:
1) Tell whether the transformation appears to be a rigid motion. Explain.
a)
b)
2) If a transformation maps GHIJ to G′H′I′J′, what is the
image of I? What is the image of GH ?
3) Point R(x, y) moves 13 units right and 14 units down.
What is a rule that describes this translation?
4) Draw the image of each figure for the given transformation.
a) Rx-axis(ABCD)
b) r (90º, O)(ABCD)
5) ΔONM has vertices O(4, 2), N(3, 6), and M(0, 3).
What are the coordinates of the vertices of
(Ry = 1 ○ T<3, 0.>)(ΔONM)
6) Is the transformation of AB with vertices A(2, 3) and
B(1, 2), first across x = 4, and then across y = 2, a
translation or a rotation? For a translation, describe the
direction and distance. For a rotation, tell the center of
rotation and the angle of rotation.
7) The point (2, 1) is the image under the translation
T<5, 4> (x, y). What is its preimage?
8) In the diagram, is one figure a reflection image, a
translation image, or a rotation image of the other?
9) Write a congruence transformation that maps one figure to the other.
B) DEF  QPR
a) ABC  FGH
10) Draw the reflection of the figure in line .
11) Decide whether the conclusion is true or false. If
false, then tell the correct image point.
If N (3,1) is reflected in the line y  2 , then
N '(1,1)
If N (2,3) is reflected in the line x  1 then N '(4,3)
12) State the segment or triangle that represents the
image.
90 clockwise rotation of AB about P
90 clockwise rotation of DE about P
90 counterclockwise rotation of GH about P
180 counterclockwise rotation of EF about P
180 clockwise rotation of DPE about P
45 counterclockwise rotation of HPA about P
13) Quadrilateral BCDE is shown on the coordinate
grid below. Reflect the figure across the line y = x to
create B’C’D’E’.
14) Write the rules for the composition of isometries
15) Write the rules for the composition of isometries
16)ABC has vertices A(-1, 2), B(1, 3), C(4, -2). Graph
the following rotation
r(180,O )
17) Your friend and her parents are visiting colleges.
They leave their home in Enid, Oklahoma, and drive
to Tulsa, which is 107 mi east and 18 mi south of Enid.
From Tulsa, they go to Norman, 83 mi west and 63 mi
south of Tulsa. Where is Norman in relation to Enid?
18) Parallelogram ABCD is shown below. Point E is
the midpoint of segment AB. Point F is the midpoint
of segment CD. What transformation would map the
parallelogram onto itself?
19) Graph ΔABC and its glide reflection image.
A. a reflection across AC
B. a reflection across EF
C. a rotation 180° about the origin
D. a rotation 180° about the center
of the parallelgoram
20) Kyle performs a transformation on a triangle. The
resulting triangle is similar but not congruent to the
original triangle. What transformation did Kyle
perform on the triangle?
(Rx = –1 ○ T<-1, 3>)(ΔABC)
21)
22) A translation is applied to ΔPQR to create ΔP’Q’R’.
Describe the translation in coordinate and function notation
23) Square ABCD is transformed to create the image A’B’C’D’, as shown below.
Circle all of the transformations that could have been performed.
o
o
o
o
A reflection across the line y = x
A reflection across the line y = -2x
A rotation of 180° about the origin
A reflection across the x axis, and then a
reflection across the y-axis
o A rotation of -270° about the origin, and
then a reflection across the x-axis.
24) Write a single transformation rule that has the same
effect as each composition of transformations
a) T<4, 7> ○ T<12, 5>
25) ΔABC has vertices A(1,1), B(2.5,3), and C(0,-3).
It is dilated by a scale factor of ½ about the origin to
create ΔA’B’C’. What is the length in units of side
B’C’?
26) In the xy-coordinate plane, ΔABC has vertices A(-4,6), B(2,6), and C(2,2). ΔDEF is shown in the graph below.
What is the scale factor that maps ΔABC to ΔDEF?