Free Printable Dilations and Similarity

1.

What is Dilation?

a)

Dilation means to enlarge or reduce

b)

Dilation means to reflect on something

c)

Dilation means to like something

d)

Dilation means to make something different by making it smaller

2.

A scale factor of less than one means

a)

that the prime image will be larger than the pre-image.

b)

That the prime image will be the same as the preimage.

c)

That you need to subtract that amount off of each side.

d)

That the prime image will be a reduction of the preimage.

3.

Definition: The figure before a transformation has occurred.

a)

Pre-image

b)

Image

c)

Translation

d)

Reflection

4.

Definition: The figure after a transformation has occurred.

a)

Pre-image

b)

Image

c)

Translation

d)

Reflection

5.

The __________ is the ratio of a length of the image to the corresponding length on the original figure.

a)

reduction

b)

enlargement

c)

scale factor

d)

center of dilation

6.

A triangle has vertices with coordinates (2,0), (3, -1) and (-2,-5). If the triangle is dilated by a scale factor of 3 with the origin as the center of dilation, what are the coordinates of the vertices of the image?

a)

(5,3), (6,2), (1,-2)

b)

(6,0), (9,-3), (-6,-15)

c)

(2/3,0), (1,-1/3), (-2/3,-5/3)

d)

(-1,-3), (0,-4), (-5,-8)

7.

Does the image show a dilation?

a)

Yes

b)

No

8.

Does the image show a Dilation?

a)

Yes

b)

No

9.

A triangle has vertices A(0,0), B(8,0), C(3,-2). Find the coordinates of the triangle after a dilation with a scale factor of 4. The dilation is (X,Y) --- (4x,4y)

a)

A(3,3), B(4,4), C(-3,-4)

b)

A(-4,8), B(6.5,8), C(7,7)

c)

A(0,0), B(32,0), C(12,-8)

10.

State the coordinate of the image of the given point B (-10,-6) under a dilation with center at the origin with the given scale factor k = 1/2.

a)

(5,3)

b)

(20,12)

c)

(-20,-12)

d)

(-5,-3)

11.

a)

1/2

b)

3/2

c)

2

d)

1

12.

a)

(-2,-2)

b)

(0,0)

c)

(1,1)

d)

(-2,-1)

13.

Dilate Point A by a scale factor of 1/2

a)

(-4,-4)

b)

(-1,-4)

c)

(-1,-1)

d)

(-2,-2)

14.

Choose the correct scale factor:

a)

2.5

b)

1.5

c)

3.5

d)

4

15.

Choose the correct scale factor:

a)

2

b)

3

c)

1/3

d)

1/2

16.

(x, y) -> (2x, 2y)
What is the coefficient 2 mean?

a)

plot 2 to the right and 2 up

b)

scale factor is 2 creating a new figure half the size

c)

scale factor is 2 making a figure twice the
original

d)

I don't understand this question : (

17.

What is the value of X?

a)

X=4

b)

X=6

c)

X=3

d)

X=2

18.

Are the triangles similar?

a)

Yes

b)

No

19.

Are the triangles similar?

a)

Yes

b)

No

20.

Similarity Ratio: _

a)

2/3

b)

1/2

c)

2

d)

3

21.

When you dilate a figure you...

a)

slide it.

b)

turn it.

c)

flip it.

d)

make it larger or smaller.

22.

All corresponding angles are congruent in similar figures.

a)

True

b)

False

23.

All corresponding sides are proportional (same ratio) in similar figures.

a)

True

b)

False

24.

Find x

a)

21

b)

27/7

c)

13

d)

18

25.

How does a dilation change the angles of a polygon?

a)

It changes by the scale factor.

b)

Dilations do not change the angles.

c)

It is impossible to answer this question. The angles change unpredictably.

d)

The angles all change to larger angles.

26.

If two figures are similar, the corresponding sides are ______________.

a)

equal

b)

congruent

c)

proportional

d)

none of these

27.

If two figures are similar their angles are______.

a)

proportional

b)

congruent

c)

supplementary

d)

complementary

28.

Calculate the value of the scale factor between the 2 triangles

a)

2.5

b)

3

c)

3.5

d)

4

29.

The pair of figures is similar. Find the missing side.

a)

x = 12

b)

x = 3

c)

x = 40

d)

x = 4

30.

Solve for X.

a)

2 ft

b)

3 ft

c)

4 ft

d)

6 ft

31.

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

32.

Are the following similar? Why or why not?

a)

Yes, because the corresponding angles are congruent.

b)

No, the numbers are even

c)

No, the sides are 2 times larger, but the width is the same.

33.

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)

34.

A triangle has vertices with coordinates (2,0), (3, -1) and (-2,-5). If the triangle is dilated by a scale factor of 3 with the origin as the center of dilation, what are the coordinates of the vertices of the image?

a)

(5,3), (6,2), (1,-2)

b)

(6,0), (9,-3), (-6,-15)

c)

(2/3,0), (1,-1/3), (-2/3,-5/3)

d)

(-1,-3), (0,-4), (-5,-8)

35.

Which of the following is the algebraic representation for a dilation?

a)

(x, y) → (x, 3y)

b)

(x, y) → (3x, 3y)

c)

(x, y) → (x, y - 3)

d)

(x, y) → (.5x, .4y)

36.

How do you write the algebraic notation when the scale factor is 1/2?

a)

(x, y) goes to (2x, 2y)

b)

(x, y) goes to (1/2x, 1/2y)

c)

(x, y) goes to (-2x, -2y)

d)

(x, y) goes to (2x, 1/2y)

37.

Given that $\Delta ABC\sim\Delta FED$ , find the value of x.

a)

x = 9

b)

x = 3.9

c)

x = - 0.26

d)

x = 9.95

38.

Let $\Delta XYZ$ be the dilated image of $\Delta ABC$ with a scale factor of k = 3. Which of the following is the correct center of dilation?

a)

(0, 0)

b)

(4, 1)

c)

(-5, 5)

d)

(1, 4)

39.

Which of the following must be true in order for $\Delta BCD\sim\Delta RST$ ?

a)

a = 12 b = 8

b)

a = 24 b = 16

c)

a = 6, b = 4

d)

a = 11, b = 13

40.

Let $\Delta A'B'C'$ be a dilation of $\Delta ABC$ with a scale factor of k= 1/2 and a center of dilation at (-4,1). Which of the following coordinates are vertices of $\Delta A'B'C'$ ? [Circle all that apply.]

a)

(-3, 2)

b)

(-2, 3)

c)

(-0.5, 0.5)

d)

(-2, 0.5) (-0.5, 0.5)

e)

(-2, -1)

41.

Let triangle EFG be a mapped image, dilated about the origin, from triangle JKL with a scale factor k=4 with J(2,2), K(3,4), L(1,0). Which of the following are the coordinates for E?

a)

(12, 16)

b)

(8, 8)

c)

(4, 4)

d)

(4, 0)

42.

Which answer shows a reflection across the y-axis?

a)

a

b)

b

c)

c

d)

d

43.

If you were to rotate ABCD 180° about the origin, what would the coordinates of A' be?

a)

(0, 0)

b)

(-5, -5)

c)

(-1, 3)

d)

(-5, 2)

44.

What would be the value of x?

a)

2

b)

4

c)

6

d)

8

45.

True or false, the ratios of the distance between the dilation point to each corresponding point is proportional.

a)

True

b)

False

46.

a)

Yes, similar

b)

No, not similar

47.

Reflections over the x-axis change the sign of the ____-__________.

a)

y-coordinate

b)

x-coordinate

c)

y-axis

d)

x-axis

48.

Reflecting over the y-axis changes the sign of the ____-_____________.

a)

x-axis

b)

x-coordinate

c)

y-coordinate

d)

none of the above

49.

Rule: (x,y) --> (x,-y)

a)

translates a figure down

b)

rotates a figure 90 degrees counterclockwise

c)

reflects a figure over the y axis

d)

reflects a figure over the x axis

50.

A triangle has coordinates of A(-8, 4), B(-4, 2) and C(-3, -3). The image has coordinates of A'(0, 8), B'(4, 6) and C'(5, 1) what transformation occurred?

a)

Dilation

b)

Reflection

c)

Rotation

d)

Translation

51.

A triangle has coordinates of A(-8, 4), B(-4, 2) and C(-3, -3). The image has coordinates of A'(8, -4), B'(4, -2) and C'(3, 3) what transformation occurred?

a)

Dilation

b)

Reflection

c)

Rotation

d)

Translation

52.

A triangle has coordinates of A(-8, 4), B(-4, 2) and C(-3, -3). The image has coordinates of A'(8, 4), B'(4, 2) and C'(3, -3) what transformation occurred?

a)

Dilation

b)

Reflection

c)

Rotation

d)

Translation

53.

Find the measure of the indicated angle.

a)

35 degrees

b)

40 degrees

c)

25 degrees

d)

30 degrees

54.

In figure below line a is parallel to line b , m∠1 = 78° , and m∠2 = 47° .Find measure of angle 9.

a)

47

b)

78

c)

133

d)

110

55.

In figure below line a is parallel to line b , m∠1 = 78° , and m∠2 = 47° .Find measure of angle 5.

a)

47

b)

78

c)

133

d)

110

56.

Line a and Line m are parallel lines cut by the transversal, line t. Determine the measure of angle x.

a)

100

b)

80

c)

110

d)

115

57.

Determine the value of angle x.

a)

90

b)

42

c)

71

d)

23

58.

Determine the value of angle y.

a)

71

b)

67

c)

75

d)

42

59.

The pair of figures is similar. Find the missing side.

a)

x = 9

b)

x = 28

c)

x = 7

d)

x = 63

60.

What is the similarity statement for the triangle pair?

a)

ΔXYZ~ΔNEW

b)

ΔXZY~ΔNWE

c)

ΔZYX~ΔENW

d)

ΔYZX~ΔNWE

Dilations and Similarity

Total questions: 60

Worksheet time: 3hrs 6mins

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