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Honors Geometry Chapter 9 Review
Name _____________________________
SHOW ALL WORK FOR FULL CREDIT!!
1.) A’B’C’D’ is the image of ABC after a translation.
a.) Write a rule for the translation.
b.) Verify that the translation is an isometry.
2.) Multiply.
5 
7  2  1
a.) 


 
 0 3   4  4 
 3 3 

0 
 1


b.)
 3  2  2  1  
 
 0  1 








3.) Use the description of a translation matrix to find the value of each variable.
 8 x  8  2 b
 4 4 y  d 5

 
c

2
 r  4  3
7 2
6 

4.) Write a matrix for the polygon. Then use matrix multiplication to find the image matrix that
represents the polygon after a reflection in the given line
a.) y = x



b.) y-axis
 
 
 
Polygon Matrix



Image Matrix



 
 
 
Polygon Matrix



Image Matrix
5.) The vertices of ABC are A(2, 1), B(1, 4), and C(4, 3). Reflect ABC in the first line.
Then reflect A'B'C in the second line. Graph A'B'C and A"B"C".
a.) In y = –1, then in x = 3
A’ = _______ B’ = _______ C’ = _______
A” = _______ B” = _______ C” = _______
7.) Draw a –120 rotation of ΔABC about P.
6.) Draw a 80 rotation of ABCDPGHK about P.
8.) Quadrilateral STUV has vertices S(–4, –2), T(–1, –1), U(1, –3), and V(–2, –5).
Find the vertices of S’T’U’V’ after the rotation about the origin.

a.) 90° 




Rotation

b.) 180° 

 
 
 
Polygon



Rotation

c.) 270° 

Image
 
 
 
Polygon



Rotation






Image
 
 
 
Polygon



Image
8.) The vertices of ΔABC are A(–4, 3), B(–1, 3), and C(–3, 1).
Graph the image of ΔABC after a composition of the transformations in the order they are listed.
a.) Translation: (x, y)  (x + 2, y – 3)
b.) Reflection: in the y – axis
Reflection: in the line x – axis
Rotation: 180° about (0, 3)
A’ = _______ B’ = _______ C’ = _______
A’ = _______ B’ = _______ C’ = _______
A” = _______ B” = _______ C” = _______
A” = _______ B” = _______ C” = _______
9.) Describe the composition of transformations.
1st: _______________________________________________________
2nd: ______________________________________________________
10.) The vertices of segment FG are F(–2, 2),G(–6, 4).
Graph the image of FG after a composition of the transformations in the order they are listed.
Rotation: 270° about (0, 0)
Rotation: 90° about (2, 0)
F’ = __________ G’ = __________
F” = __________ G” = __________
11.) a.) Determine whether the figure has rotational symmetry.
b.) If so, describe the rotations that map the figure onto itself.
i.)
ii.)
iii.)
a.) __________
a.) __________
a.) __________
b.) ____________________
b.) ____________________
b.) ____________________
12.) Use a straightedge to construct each dilation.
a.) k =2; Center at H
b.) k =
1
; Center at J
2
13.) The vertices of ABCDE are A(–6, 0), B(–3, 0), C(0, –3), D(–3, –6), and E(–6, –3).
Graph the image of ABCDE after a composition of the transformations in the order they are listed.
a.) Translation: (x, y)  (x + 9, y – 6)
Dilation: Centered at (0, 0) with k = ⅓
b.) Dilation: Centered at (0, 0) with k = ½
Reflection: in the x – axis
A’ = _______ B’ = _______ C’ = _______
A’ = _______ B’ = _______ C’ = _______
D’ = _______ E’ = _______
D’ = _______ E’ = _______
A” = _______ B” = _______ C” = _______
A” = _______ B” = _______ C” = _______
D” = _______ E” = _______
D” = _______ E” = _______