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Transformations and Dilations

Total questions: 57

Worksheet time: 2hrs 49mins

Name
Class
Date
1.
Which of the statements is true about the graphed triangles?
a)
They are similar, because one can be obtained by dilating the other about the origin with a scale factor of 2.
b)
They are similar, because one can be obtained by dilating the other about the origin with a scale factor of 1/2.
c)
They are not similar, because one can be obtained by dilating the other about the origin with a scale factor of 2.
d)
They are not similar, because one can be obtained by dilating the other about the origin with a scale factor of 1/2.
2.
Rectangle ABCD is undergoing a series of transformations. Which of the following transformations will NOT cause the resulting rectangle  to maintain congruence with rectangle ABCD? 
a)
Translation 3 units left, then translation 7 units down. 
b)
Dilation by a scale factor of 3, then dilation by a scale factor of 3.
c)
Dilation by a scale factor of 2, then dilation by a scale factor of 1/2.
d)
Translation 4 units right, then translation 6 units up. 
3.
Figures ABC and DEF are similar.  Which series of transformations of figure ABC shows that ABC and DEF are Similar? 
a)
90 degree clockwise rotation, then dilation by a scale factor of ¾
b)
90 degree counterclockwise rotation, then dilation by a scale factor of ¾
c)
Reflection across a vertical line, then dilation by a scale factor of ¾
d)
Reflection across a horizontal line, then dilation by a scale factor of ¾
4.
Figures A and B are similar.  Which transformation of figure A shows that A and B are similar?
a)
Translation 3 units up
b)
Translation 3 units down
c)
Dilation by a scale factor of 3
d)
Dilation by a scale factor of 1/3
5.
Dilate the figure by a scale factor of 3 with the origin as the center of dilation. What are the coordinates of the image?
A(3,3) B(6,6) C(9,3)
a)
A'(9,9) B'(18,18) C'(27,9)
b)
A'(6,6) B'(9,9) C'(12,6)
c)
A'(0,0) B'(3,3) C'(6,0)
d)
A'(1,1) B'(2,2) C'(3,1)
6.

Which is an Example of a dilation

a)
b)
c)
d)
7.
Which rule shows the transformation?
a)
(x, y) ----> (0.5x, 0.5y)
b)
(x, y) ----> ( 2 + x, 2 + y)
c)
(x, y) -----> (2x, 2y)
d)
(x, y) -----> (3x, 3y)
8.

Reflect ΔXYZ over the x-axis.

X(0 , -3) ; Y(-2 , 4) ; Z(1 , 3)

a)

X'(0 , 3) ; Y'(-2 , -4) ; Z'(1 , -3)

b)

X'(0 , -3) ; Y'(2 , 4) ; Z'(-1 , 3)

c)

X'(-3 , 0) ; Y'(4 , -2) ; Z'(3 , 1)

d)

X'(0 , -3) ; Y'(2 , -4) ; Z'(-1 , 3)

9.

Reflect ΔXYZ over the y-axis.

X(0 , -3) ; Y(-2 , 4) ; Z(1 , 3)

a)

X'(0 , 3) ; Y'(-2 , -4) ; Z'(1 , -3)

b)

X'(0 , -3) ; Y'(2 , 4) ; Z'(-1 , 3)

c)

X'(-3 , 0) ; Y'(4 , -2) ; Z'(3 , 1)

d)

X'(0 , -3) ; Y'(-2 , 4) ; Z'(-1 , 3)

10.

Reflect ΔXYZ over the line y = x.

X(0 , -3) ; Y(-2 , 4) ; Z(1 , 3)

a)

X'(0 , 3) ; Y'(-2 , -4) ; Z'(1 , -3)

b)

X'(0 , -3) ; Y'(2 , -4) ; Z'(-1 , 3)

c)

X'(-3 , 0) ; Y'(4 , -2) ; Z'(3 , 1)

d)

X'(0 , -3) ; Y'(2 , 4) ; Z'(-1 , 3)

11.

Reflect ΔXYZ over the line y = -x.

X(0 , -3) ; Y(-2 , 4) ; Z(1 , 3)

a)

X'(0 , 3) ; Y'(-2 , -4) ; Z'(1 , -3)

b)

X'(0 , -3) ; Y'(2 , 4) ; Z'(-1 , 3)

c)

X'(-3 , 0) ; Y'(4 , -2) ; Z'(3 , 1)

d)

X'(3 , 0) ; Y'(-4 , 2) ; Z'(-3 , -1)

12.

Rotate ΔPQR 90o counterclockwise about the origin.

P(-5 , 2) ; Q(1 , 5) ; R(3 , -2)

a)

P'(-2 , -5) ; Q'(-5 , 1) ; R'(2 , 3)

b)

P'(2 , -5) ; Q'(5 , 1) ; R'(-2 , 3)

c)

P'(2 , 5) ; Q'(5 , -1) ; R'(-2 , -3)

d)

P'(-2 , 5) ; Q'(-5 , -1) ; R'(2 , -3)

13.

Rotate ΔPQR 180o about the origin.

P(-5 , 2) ; Q(1 , 5) ; R(3 , -2)

a)

P'(-2 , -5) ; Q'(-5 , 1) ; R'(2 , 3)

b)

P'(-5 , -2) ; Q'(1 , -5) ; R'(3 , -2)

c)

P'(2 , 5) ; Q'(5 , -1) ; R'(-2 , -3)

d)

P'(5 , -2) ; Q'(-1 , -5) ; R'(-3 , 2)

14.

Rotate ΔPQR 270o counterclockwise about the origin.

P(-5 , 2) ; Q(1 , 5) ; R(3 , -2)

a)

P'(-2 , -5) ; Q'(-5 , 1) ; R'(2 , 3)

b)

P'(-5 , -2) ; Q'(1 , -5) ; R'(3 , -2)

c)

P'(2 , 5) ; Q'(5 , -1) ; R'(-2 , -3)

d)

P'(5 , -2) ; Q'(-1 , -5) ; R'(-3 , 2)

15.

The center of dilation is the origin. Dilate ΔEFG given a scale factor of 3.

E(4 , 9) ; F(-3 , 12) ; G(2 , -8)

a)

E'(4/3 , 3) ; F'(-1 , 4) ; G'(2/3 , -8/3)

b)

E'(12 , 27) ; F'(-9 , 36) ; G'(6 , -24)

c)

E'(7 , 12) ; F'(0 , 15) ; G'(5 , -5)

d)

E'(1 , 6) ; F'(-6 , 9) ; G'(-1 , -11)

16.

Which of the 4 transformations from this unit is NOT a Congruence Transformation ?

a)

Dilation

b)

Translation

c)

Rotation

d)

Reflection

17.
Identify the transformation from ABCD to A'B'C'D'.
a)
Translation
b)
Reflection across the x-axis
c)
Reflection across the y-axis
d)
90o counter clockwise rotation
18.
Which answer represents a reflection across the x-axis, using the algebraic rule (x,y) --> (x, -y)?
a)
d
b)
c
c)
b
d)
a
19.
How do you represent a translation Algebraically? 
a)
(-y, -x)
b)
(x + a, y + b)
c)
(-x , -y)
d)
(ax, by)
20.
When you translate,
(x - 4, y + 3) the figure will move _____.
a)
4 units left and 3 units right
b)
4 units left and 3 units up
c)
4 units down and 3 units up
d)
4 units down and 3 units down
21.
A slide is also called a _________.
a)
Translation
b)
Reflection
c)
Rotation
d)
Transformation
22.
A turn is also called a ___________.
a)
Translation
b)
Reflection
c)
Rotation
d)
Transformation
23.
All angles in similar figures are congruent.  
a)
True
b)
False
24.
Identify the transformation from ABC to A'B'C'.
a)
(x+8, y+4)
b)
(x-8, y-4)
c)
(x+4, y+8)
d)
(x-4, y-8)
25.
A turn is also called a ___________.
a)
Translation
b)
Reflection
c)
Rotation
d)
Transformation
26.
If the triangle is transformed following the rule (x,y)⊣(x,-y), what transformation is modeled?
a)
Dilation
b)
Reflection
c)
Translation
d)
Rotation
27.
Name the image of C(6, -4) under a rotation 90 degrees counterclockwise about the origin.
a)
C'(4, 6)
b)
C'(-4, -6)
c)
C'(6, 4)
d)
C'(-6, -4)
28.
Given C(2, 9), under which reflection is C'(-2, 9)?
a)
reflected in the x-axis
b)
reflected in the y-axis
c)
reflected in the line x = 2
d)
reflected in the line y = x
29.
Two objects that are the same shape but not the same size are _______.
a)
Congruent
b)
Vertical
c)
Similar
d)
Complementary 
30.
A dilation with a scale factor of 1/3 is a reduction. 
a)
True 
b)
False
31.
A dilation with a scale factor of 2 is a reduction. 
a)
True
b)
False
32.

What is the proper term for rotating to the left?

a)

Clockwise

b)

Counter-clockwise

c)

Turn

d)

Spin

33.

Which way do you rotate if you turn to the right?

a)

Clockwise

b)

Counter-clockwise

c)

upside down

d)

flip-flop

34.

If an image were reflected over the x-axis from quadrant 1 to quadrant 4, what would you need to do to reflect it to quadrant 3?

a)

Translate it two units to the right

b)

Rotate 20 degrees CCW

c)

Reflect it over the x-axis

d)

Reflect it over the y-axis

35.
C(-6, 2) and B(-1, -1)
Reflect over the line y = x
a)
C' (-6, 2), B' (-1, -1)
b)
C' (6, 2), B' (1, -1)
c)
C' (2, -6), B' (-1, -1)
d)
C' (-6, -2), B' (-1, -1)
36.
A(-2, 2) and B(3, 2)
Reflect over the x-axis 
a)
A' (-2, 2), B' (3, 2)
b)
A' (-2, -2), B' (3, -2)
c)
A' (2, -2), B' (-3, -2)
d)
A' (2, -2), B' (2, 3)
37.
A(-2, 2) and B(3, 2) 
Dilate k = 1 
a)
A' (-2, 2), B' (3, 2)
b)
A' (-4, 4), B' (6, 4)
c)
A' (2, -2), B' (-3, -2)
d)
A' (2, -2), B' (2, 3)
38.
C(-6, 2) and B(-1, -1)
Translate (x, y) -> (x + 3, y - 1)
a)
C' (-3, 1), B' (2, -2)
b)
C' (3, -1), B' (-2, -4)
c)
C' (-9, 1), B' (-4, -2)
d)
C' (-7, 1), B' (-2, -2)
39.
C(-6, 2) and B(-1, -1)
Translate (x, y) -> (x - 1, y - 3)
a)
C' (-6, 2), B' (-1, -1)
b)
C' (-7, -1), B' (-2, -4)
c)
C' (-5, 5), B' (0, 2)
d)
C' (-7, 1), B' (-2, -2)
40.
After a figure has been transformed, we call the new figure the...
a)
Image
b)
Different shape
c)
Figure that moved
d)
Prime
41.
In translations, the image and the pre-image are always
a)
parallel
b)
next to each other
c)
congruent
d)
opposite
42.
Translations, rotations, and reflections are three different types of what?
a)
Transformations
b)
Geometry
c)
Vectors
d)
Shapes
43.
The mathematical term for the line that you reflect a shape over is the...
a)
Mirror
b)
Reflective tape
c)
Line that you reflect over
d)
Line of reflection
44.
How is Quadrilateral EFGH translated to E'F'G'H'?
a)
6 down
b)
6 down, 1 right
c)
6 down, 3 left
d)
8 down, 1 right
45.
Which answers are showing a reflection?
a)
a and c
b)
b and c
c)
c and d
d)
a and d
46.
How is triangle ABC being translated to triangle A'B'C'?
a)
up 3, left 8
b)
up 9, left 4
c)
down 3, right 8
d)
down 9, right 4
47.
The following is a ...
a)
Translation
b)
Reflection
c)
Rotation
d)
Dilation
48.
When you translate, (x-4,y) will move _____.
a)
4 units right
b)
4 units left
c)
4 units up
d)
4 units down
49.
When you translate, (x,y+6) will move _____.
a)
6 units right
b)
6 units left
c)
6 units up
d)
6 units down
50.
Are the following similar? Why or why not?
a)
Yes. All pairs of corresponding angles are congruent.
b)
No, the corresponding angles are not equal.
c)
No, the ratios of the corresponding sides are not equal.
51.
Tell whether the two figures are congruent.
a)
Yes, same size and same shape
b)
No, same shape but different sizes
c)
No, different size and different shapes
52.
Are these two shapes congruent or not congruent?
a)
congruent
b)
not congruent
53.
Are these shapes congruent or not congruent?
a)
congruent
b)
not congruent
54.
A type of transformation where a geometric figure slides horizontally, vertically, or both. What type of transformation is this? 
a)
dilation
b)
translation
c)
rotation
d)
reflection
55.
Write a rule for the translation.
a)
 (x -1, y  + 2)
b)
 (x -2, y  + 1)
c)
 (x +2, y  - 1)
d)
(x +1, y  -  2)
56.
The original figure prior to a transformation.
a)
Pre-image
b)
Image
57.
All angles in similar figures are congruent.  
a)
True
b)
False

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