Free Printable #7-Dilations

1.

Question 1

An image is dilated by a scale factor of $\frac{1}{4}$ . This will result in ____________ of the original image.

a)

an enlargement

b)

a reduction

2.

Question 2

An image is dilated by a scale factor of $\frac{5}{2}$ . This will result in ____________ of the original image.

a)

an enlargement

b)

a reduction

3.

Question 3

Find the scale factor that was used to dilate the point below:

$\left(12,6\right)\rightarrow\left(4,2\right)$

a)

$3$

b)

$\frac{1}{3}$

c)

$\frac{1}{4}$

4.

Question 4

A triangle has the following vertices:

A(3,6), B(3,3), and C(6,3)

If the triangle undergoes a dilation using the origin as the center of dilation with a scale factor of $\frac{4}{3}$ , what will be the location of A'?

a)

(4, 8)

b)

(8, 4)

c)

(4, 4)

5.

Question 5

What is the scale factor of the dilation that maps $\Delta ABC\rightarrow\Delta A'B'C'$ ?

a)

$\frac{2}{3}$

b)

$\frac{3}{2}$

c)

$2$

6.

Question 6

In the diagram, ΔR'S'T' is the image of ΔRST. Which type of transformation is shown?

a)

translation

b)

reflection

c)

dilation

7.

Question 7

Triangle PQR is shown.

What are the coordinates of P' when ΔPQR is dilated by a scale factor of 3 using the origin as the center?

a)

$\left(6,\ 18\right)$

b)

$\left(\frac{2}{3},\ 3\right)$

c)

$\left(18,\ 6\right)$

8.

Question 8

ΔMNP is shown.

The triangle is dilated by a factor of 2.5 using the origin as the center of dilation to form ΔM'N'P'.

What is the length of the line segment $\overline{P'N'}$ ?

a)

5 units

b)

10 units

c)

10 units

9.

Question 9

Which pair of figures must be similar?

a)

b)

c)

10.

Question 10

Which of the following is similar to the given rectangle?

(Figures are NOT drawn to scale.)

a)

b)

c)

11.

A dilation is which of the following:

a)

only an enlargement

b)

only a reduction

c)

Either an enlargement or a reduction

d)

Neither an enlargement or a reduction

12.

A dilation produces a congruent figure

a)

True

b)

False

13.

When a dilation has a scale factor greater than one, the dilation is an enlargement.

a)

True

b)

False

14.

When the scale factor of a dilation is less than one, the dilation is a reduction.

a)

True

b)

False

15.

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

a)

reduction

b)

enlargement

c)

scale factor

d)

center of dilation

16.

State the coordinate of the image of the given point B (4,9) under a dilation with center at the origin with the given scale factor of 2.

a)

B' (2 , 4.5)

b)

B' (-8 ,-18)

c)

B' (8 ,18)

d)

B' (9 ,4)

17.

The point (8, 12) was dilated to become point (2, 3). What was the scale factor?

a)

½

b)

¼

c)

4

d)

2

18.

What scale factor was used to produce the image?

a)

2

b)

-2

c)

¹/₂

d)

1

19.

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)

20.

Choose the correct scale factor:

a)

2

b)

3

c)

1/3

d)

1/2

21.

The point A (8, 12) was dilated to become point A' (2, 3). What was the scale factor?

a)

½

b)

¼

c)

4

d)

2

22.

In a dilation what mathematical operation is used with the scale factor?

a)

addition

b)

subtraction

c)

multiplication

d)

division

23.

If your SF = 0.8, what type of dilation is it?

a)

Reduction

b)

Enlargement

24.

If your SF = 6/5, what type of dilation is it?

a)

Reduction

b)

Enlargement

25.

Dilate Point B by a scale factor of 3:

a)

(12,0)

b)

(12,12)

c)

(4,3)

d)

(0,12)

26.

Does the image show a dilation?

a)

Yes

b)

No

27.

Does the image show a Dilation?

a)

Yes

b)

No

28.

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)

29.

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)

30.

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)

31.

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)

32.

A dilation is which of the following:

a)

only an enlargement

b)

only a reduction

c)

Either an enlargement or a reduction

d)

Neither an enlargement or a reduction

33.

How do you write the algebraic notation when the scale factor is 3?

a)

(x, y) goes to (1/3x, 1/3y)

b)

(x, y) goes to (-3x, -3y)

c)

(x, y) goes to (x + 3, y + 3)

d)

(x, y) goes to (3x, 3y)

34.

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)

35.

Dilate Point B by a scale factor of 3:

a)

(12,0)

b)

(12,12)

c)

(4,3)

d)

(0,12)

36.

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)

37.

In a dilation what mathematical operation is used with the scale factor?

a)

addition

b)

subtraction

c)

multiplication

d)

division

38.

A scale factor of less than one means

a)

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

b)

That the image will be the same as the pre-image.

c)

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

d)

That the image will be a reduction of the pre-image.

39.

a)

A

b)

B

c)

C

d)

D

40.

a)

E

b)

F

c)

G

d)

H

41.

a)

A

b)

B

c)

C

d)

D

42.

Congruent figures are figures that are the SAME size and the SAME shape.

A dilation produces a congruent figure.

a)

True

b)

False

43.

In this figure, triangle TRS is the (a) , triangle T'R'S' is the (b) and a(n) (c) occurred.

Choose from the below words

pre-image

image

enlargement

reduction

spin

flip

44.

Which of the following statements is true about the scale factor (k) for this dilation?

a)

$k>1$

b)

$k=1$

c)

$0<k<1$

45.

In this figure, triangle ABC is the (a) and triangle A'B'C' is the (b) . The scale factor for this dilation is (c) . A(n) (d) occurred.

Choose from the below words

pre-image

image

2

reduction

enlargement

None of the above

1/2

46.

Quadrilateral NDPM was dilated to quadrilateral N'D'P'M'. What was the scale factor for this dilation?

a)

2

b)

3

c)

1/3

d)

1/2

47.

The point (8, 12) was dilated to become point (2, 3). What was the scale factor?

a)

½

b)

¼

c)

4

d)

2

48.

If triangle ABC was dilated by a scale factor of 3, with the origin as the center of dilation, what would the coordinates of B' be?

a)

(12,0)

b)

(12,12)

c)

(4,3)

d)

(0,12)

49.

What is the correct scale factor for this dilation?

a)

2.5

b)

1.5

c)

3.5

d)

4

50.

State the coordinates of point C after a dilation with a scale factor of 1/2 and center of dilation at point P.

a)

(-6, 1)

b)

(-3, -2)

c)

(1, -6)

d)

(-2, -3)

51.

A triangle has vertices with coordinates A(2,0), B(3, -1) and C(-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 new image?

a)

A'(5,3), B'(6,2), C'(1,-2)

b)

A'(6,0), B'(9,-3), C'(-6,-15)

c)

A'(2/3,0), B'(1,-1/3), C'(-2/3,-5/3)

d)

A'(-1,-3), B'(0,-4), C'(-5,-8)

52.

State the coordinates of point B after a dilation, with the center of dilation at the origin, and a scale factor of 1/2.

a)

(1.5,-4)

b)

(-1.5,1)

c)

(-1,-1.5)

d)

(-2,-2)

53.

State the coordinates of point A after a dilation, with the center of dilation at (0,0), and a scale factor of 1/2.

a)

(2,2)

b)

(8,8)

c)

(0,12)

d)

(4,12)

54.

The red triangle has been dilated by a scale factor of 1/4, with the center of dilation at (0,0), which triangle is it's new image?

a)

green triangle

b)

red triangle

c)

black triangle

d)

none of these

55.

Which of the following algebraic rules represents an enlargement? Select all that apply.

a)

(x, y) --> (3x, 3y)

b)

(x, y) --> (0.5x, 0.5y)

c)

(x, y) --> (0.75x, 0.75y)

d)

(x, y) --> (0.999x, 0.999y)

e)

(x, y) --> (5x, 5y)

56.

Point A is ( 7, 3) and Point A' is ( 21, 9). What is the algebraic rule for this dilation if the center of dilation is at the origin?

a)

$f\left(x,y\right)\ \rightarrow\left(\frac{1}{3}x,\ \frac{1}{3}y\right)$

b)

$f\left(x,y\right)\rightarrow\left(3x,\ 3y\right)$

c)

$f\left(x,y\right)\ \rightarrow\left(x+14,\ y+6\right)$

d)

$f\left(x,y\right)\ \rightarrow\ \left(0x,\ 0y\right)$

#7-Dilations

Total questions: 56

Worksheet time: 3hrs 56mins

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