NAME:______________________________
DATE:________________________
Geometry – Review: Transformations
1. Which diagram is a NOT a mapping?
Pre-Image
A)
Image
Pre-Image
B)
Pre-Image
Image
C)
Pre-Image
Image
Image
D)
ANSWER: D
2. Which of the following is not an isometric transformation?
A) Reflection
B) Dilation
C) Rotation
D) Translation
ANSWER: B
3. Which of the following is a non-isometric transformation?
A) T ( x, y)      ( x  4, y  3)
B) T ( x, y)      ( y, x)
C) T ( x, y)      (2 x, 2 y)
D) T ( x, y)      ( x  5, y   )
ANSWER: C
4. Given coordinate rule, T ( x, y)      ( x, x  y) determine the image of A(-4,5)?
2
5. Given coordinate rule, T ( x, y)      ( x , 5) determine the image of A(-2,2)?
ANSWER: ( -4, 1)
ANSWER: ( -4, -5)
6. Given coordinate rule, T ( x, y)      ( x  2, y  6) determine the pre-image of A’(-2,2)? ANSWER: (0, -4)
7. What is the difference between mapping and transformations?
ANSWER: In a mapping, the number of points in the image must be less than or equal to the number of points in the
Pre-image. In a transformation, the number of points in the image must be equal to the number of points in the preimage.
8. Give an example of a non-isometric transformation and an isometric transformation. Explain the difference.
ANSWER: Non-isometric: Dilation
the same.
Isometric: Translation.
An isometric translation keeps the size and shape
9. Determine the vector that is represented by the given arrow.
a)
< __2_ , _-4_>
b)
< -5 , 0 >
10. Write the translation coordinate rule from the given vector.
T(x,y) ----> ( x-4, y + 1)
11. Determine the translation rule from the pre-image and image.
a) A (-5,5)
A’ (1,9)
T (x,y) ------------- > ( x+6, y + 4 )
b) A (-8,1)
A’ (-7,2)
T (x,y) ------------- > ( x + 1, y + 1)
12. Given a translation rule, determine the missing point.
a) T (x,y) ------- > (x - 1, y – 2)
A (-1,4)
A’ ( -2, 2)
b) T (x,y) ------- > (x - 8, y + 1)
A (5,1)
A’ ( -3, 2)
c) T (x,y) ------- > (x + 4, y + 4)
A ( 7, 3 )
A’ (3,-1)
13. Determine the rotational symmetry order and angle of rotation for each diagram. If none, write 1.
a) ANSWER: Order = 5, Angle = 72◦
Angle = 120
b) ANSWER: Order = 3,
14. Determine if the following angles would result in a rotational symmetry for the given regular polygons.
a)
Regular Hexagon, 1380◦
b) Regular Octagon, 765◦
c) Regular Decagon, 254◦
ANSWER: YES
ANSWER: YES
ANSWER: NO
15. Perform the following reflections.
a)
b)
16. Determine the pre-image coordinates, then reflect it, and determine the image coordinates.
a) A = (
-5,7)
rxaxis (A)
n
A ‘ = ( -5 , -7)
A
b) E = (5,5)
ryaxis (E )
m
E
E ‘ = ( -5 , 5)
C
D
c) C = (0,3)
rM (C )
C‘=(0,7)
B
17. Determine the name of the point that meets the given conditions.
F
a) rn (A)
B
b) rr (C )
A
m
F
A
c) rs (D)
A
d) rm (D)
B
18. G( x,y) -------> (-x,y) is a reflection over the x axis.
T or F
ANSWER: T
19. R (x,y) -------> (-x,-y) is a reflection over the line y = x.
T or F
ANSWER: F
20. A reflection of A (-5,4) over the y axis results in A’ (5,4)
T or F
ANSWER: T
21. A reflection of A (2,10) over the x axis results in A’ (-2,10)
T or F
ANSWER: F
r
B
G s
E
D
n
H
C
22. A reflection of A (4,5) over the line y = x results in A’ (-4,-5) ANSWER: F
T or F
23. Perform the following rotation.
a) RO,90 (ABC )
24. Rotate the triangle about the origin the given angle of rotation. Determine the coordinates of the image and plot
them.
D
E
A
RO,90 (ABC )
a) A = (4,6)
RO,90 (ABC ) A ‘ = ( -6, 4 )
b) B = (7,0)
RO,90 (ABC ) B ‘ = ( 0, 7 )
c) C = (3,3)
RO,90 (ABC ) C ‘ = ( -3, 3 )
25. Use a compass and straight edge to construct the following reflection over line m.
a) rm (ABC )