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Dilations

Total questions: 91

Worksheet time: 5hrs 35mins

Name
Class
Date
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 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)
3.
Choose the correct scale factor:
a)
2
b)
3
c)
1/3
d)
1/2
4.
Dilate Point B by a scale factor of 3:
a)
(12,0)
b)
(12,12)
c)
(4,3)
d)
(0,12)
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.
Find missing side
a)
5
b)
7
c)
9
d)
11
7.

What type of transformation is this?

a)

rotation

b)

translation

c)

reflection

d)

dilation

8.

What type of transformation is this?

a)

rotation

b)

translation

c)

reflection

d)

dilation

9.

What type of transformation is this?

a)

rotation

b)

translation

c)

reflection

d)

dilation

10.

What type of transformation is this?

a)

rotation

b)

translation

c)

reflection

d)

dilation

11.

This type of transformation changes the size:

a)

rotation

b)

translation

c)

reflection

d)

dilation

12.

Which is the pre-image (first one)?

a)

Purple

b)

Blue

13.

Translated figures are always __________________.

a)

Congruent

b)

Bigger

c)

Smaller

d)

Rotated

14.

A reflection ____________________.

a)

turns a figure around a point.

b)

slides an object form one place to another.

c)

flips or mirrors an object across a line.

d)

changes the size of an object.

15.

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

16.
Definition: The figure before a transformation has occurred. 
a)
Pre-image
b)
Image
c)
Translation
d)
Reflection
17.
What scale factor was used to produce the image?
a)
2.5
b)
1.5
c)
3.5
d)
4
18.
A dilation always produces a similar figure. Similar figures have the same ______ but different ______. 
a)
measure; shapes
b)
sizes; shapes
c)
value; measures
d)
shape; sizes
19.
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 nor a reduction
20.
State the coordinates of the image of point B after a dilation with a scale factor of 2 and centered at point A.
a)
(-4,2)
b)
(-8,4)
c)
(-4,6)
d)
(-2,-2)
21.
Definition: The figure after a transformation has occurred. 
a)
Pre-image
b)
Image
c)
Translation
d)
Reflection
22.
A dilation always produces a congruent figure.
a)
True
b)
False
23.
Did the image enlarge, reduce or none of the above?
a)
Enlarge
b)
Reduce
c)
None of the above
24.
Does the image show a Dilation? If yes, did the image enlarge, reduce or none of the above?
a)
Yes, enlarge
b)
Yes, reduce
c)
No
25.
What scale factor was used to produce the image?
a)
1
b)
7
c)
18
d)
49
26.
What scale factor was used to produce the image?
a)
2
b)
-2
c)
1/2
d)
1
27.
Find the measure of x:
a)
6
b)
24
c)
33
d)
36
28.
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)
29.
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 r = 2.
a)
(2,4.5)
b)
(-8,-18)
c)
(8,18)
d)
(9,4)
30.
State the coordinates of the image of point C after a dilation with a scale factor of 1/2 and center point P.
a)
(-6, 1)
b)
(-3, -2)
c)
(1, -6)
d)
(-2, -3)
31.
The red triangle has been dilated by a scale factor of 1/4 about the origin, which triangle is it's new image? 
a)
green triangle 
b)
red triangle 
c)
black triangle
d)
none of these 
32.
Under a dilation, which scale factor will result in a congruent image?
a)
-2
b)
0
c)
1
d)
1/2
33.

What are the coordinates for the center of dilation?

a)

(0, 0)

b)

(-3, -1)

c)

(-12, 6)

d)

(-3, -3)

34.
Find the measure of x:
a)
6
b)
24
c)
33
d)
36
35.
Which of the following are Dilations?
a)
(x, y) → (x, 3y)
b)
(x, y) → (3x, 3y)
c)
(x, y) → (x, y - 3)
d)
(x, y) → (.5x, .4y)
36.
When you translate, (x,y+6) will move _____.
a)
6 units right
b)
6 units left
c)
6 units up
d)
6 units down
37.
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)
38.
The point (8, 12) was dilated to become point (2, 3). What was the scale factor?
a)
½
b)
¼
c)
4
d)
2
39.
Dilate Point B by a scale factor of 1/2
a)
(1.5,-4)
b)
(-1.5,1)
c)
(-1,-1.5)
d)
(-2,-2)
40.
Dilate Point B by a scale factor of 3:
a)
(12,0)
b)
(12,12)
c)
(4,3)
d)
(0,12)
41.
Does the image show a dilation?
a)
Yes
b)
No
42.
 A dilation can produce a larger figure or a(n)______
use a synonym for larger
a)
reduction
b)
enlargement
c)
scale factor
d)
center of dilation
43.
A dilation can produce a smaller figure or a(n)______
use a synonym for smaller
a)
reduction
b)
enlargement
c)
scale factor
d)
center of dilation
44.
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 k = 2.
a)
(2,4.5)
b)
(-8,-18)
c)
(8,18)
d)
(9,4)
45.
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)
46.
Robbie made a scale drawing of a neighborhood park. A soccer field in the park is 14 inches long in the drawing. The actual field is 98 yards long. What is the scale of the drawing?1 inch = _ yards
a)
1372
b)
5
c)
14
d)
7
47.
a)
A
b)
B
c)
C
d)
D
48.
The red triangle has been dilated by a scale factor of 1/4, which triangle is it's new image? 
a)
green triangle 
b)
red triangle 
c)
black triangle
d)
none of these 
49.
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)
50.
If the scale factor is less than one, the new figure will be
a)
an enlargement
b)
a reduction
c)
a scale factor
d)
bigger
51.
Choose the correct scale factor:
a)
2
b)
3
c)
1/3
d)
1/2
52.
Dilate Point B by a scale factor of 1/2
a)
(1.5,-4)
b)
(-1.5,1)
c)
(-1,-1.5)
d)
(-2,-2)
53.
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)
54.
Dilate Point B by a scale factor of 3:
a)
(12,0)
b)
(12,12)
c)
(4,3)
d)
(0,12)
55.
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
56.
In a dilation what mathematical operation is used with the scale factor?
a)
addition 
b)
subtraction 
c)
multiplication 
d)
division 
57.
A dilation is which of the following: 
a)
An enlargement
b)
A reduction
c)
Either an enlargement or a reduction
d)
Neither an enlargement or a reduction
58.
The corresponding point for a pre- image that has one vertice at ( 2, 3) and a scale factor of 2 would be at (4, 6).
a)
True in all cases. It doesn't matter where the center of dilation is located. You simply multiply the coordinates by the scale factor. 
b)
False. You can't use the scale factor to find the coordinates of the corresponding vertice.
c)
True, assuming that the center of dilation is at the origin.
d)
False, the corresponding vertice would have coordinates of (4, 5)
59.

Is this an enlargement or a reduction?

a)

Enlargement

b)

Reduction

60.

Is this an enlargement or a reduction?

a)

Enlargement

b)

Reduction

61.

Is this an enlargement or a reduction?

a)

Enlargement

b)

Reduction

62.

Is this an enlargement or a reduction?

a)

Enlargement

b)

Reduction

63.

Triangle E’F’G’ is a dilation of triangle EFG.


Which rule best represents the dilation shown?

a)

(x, y) --> (2x, 2y)

b)

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

c)

(x, y) --> (x + 2, y - 2)

d)

(x, y) --> (2x, 0.5y)

64.

Quadrilateral WXYZ was dilated with the origin as the center to create quadrilateral W’X’Y’Z’.


Which rule best represents the dilation that was applied to quadrilateral WXYZ to create quadrilateral W’X’Y’Z’?

a)

(x, y) --> (0.4x, 0.4y)

b)

(x, y) --> (x + 3, y + 2)

c)

(x, y) --> (2.5x, 2.5y)

d)

(x, y) --> (x - 3, y - 2)

65.

Trapezoid A’B’C’D’ is the dilation of trapezoid ABCD.


Which algebraic representation shows this dilation?

a)

(x, y) --> (2x, 2y)

b)

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

c)

(2x, 2y) --> (x, y)

d)

(x, y) --> (3x, 2y)

66.

Triangle ABC is dilated by a scale factor of one-half to form Triangle A’B’C’ with the origin as a center of dilation.


Which rule represents this dilation?

a)

(x, y) --> (2x, 2y)

b)

(x, y) --> (1/2x, 1/2y)

c)

(2x, 2y) --> (x, y)

d)

(x, y) --> (1/3x, 1/3y)

67.

Triangle A’B’C’ is the dilation of triangle ABC.


Which algebraic representation shows this dilation?

a)

(x, y) --> (1/2x, 1/2y)

b)

(x, y) --> (2x, 2y)

c)

(x, y) --> (x + 1/2, y)

d)

(x, y) --> (1/2x, y)

68.

Triangle A’B’C’ is the dilation of triangle ABC.


Which algebraic representation shows this dilation?

a)

(x, y) --> (1/2x, 1/2y)

b)

(x, y) --> (2x, 2y)

c)

(x, y) --> (x + 1/2, y)

d)

(x, y) --> (1/2x, y)

69.

Triangle A’B’C’ is the dilation of triangle ABC.


Which algebraic representation shows this dilation?

a)

(x, y) --> (2x, 2y)

b)

(x, y) --> (1/3x, 1/3y)

c)

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

d)

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

70.

A line segment is dilated by a scale factor of 2 centered at a point not on the line segment. Which statement regarding the relationship between the given line segment and its image is true?

a)

The line segments are perpendicular, and the image is one-half of the length of the given line segment.

b)

The line segments are perpendicular, and the image is twice the length of the given line segment.

c)

The line segments are parallel, and the image is twice the length of the given line segment.

d)

The line segments are parallel, and the image is one-half of the length of the given line segment

71.

The line whose equation is 3x – 5y = 4 is dilated by a scale factor of 5/3 centered at the origin. Which statement is correct?

a)

The image of the line has the same slope as the pre-image but a different y-intercept.

b)

The image of the line has the same y-intercept as the pre-image but a different slope.

c)

The image of the line has the same slope and the same y-intercept

as the pre-image.

d)

The image of the line has a different slope and a different y-intercept from the pre-image.

72.

A line that passes through the points whose coordinates are (1,1) and (5, 7) is dilated by a scale factor of 3 and centered at the origin. The image of the line

a)

is perpendicular to the original line

b)

is parallel to the original line

c)

passes through the origin

d)

is the original line

73.

A three-inch line segment is dilated by a scale factor of 6 and centered at its midpoint. What is the length of its image?

a)

9 inches

b)

2 inches

c)

15 inches

d)

18 inches

74.

Line segment A'B' whose endpoints are (4, -2) and (16, 14) is the image of AB after a dilation of 1/2 centered at the origin. What is the length of AB?

a)

5

b)

10

c)

20

d)

40

75.

In the diagram below, CD is the image of AB after a dilation of scale factor k with center E. Which ratio is equal to the scale factor k of the dilation?

a)

EC : EA

b)

BA : EA

c)

EA : BA

d)

EA : EC

76.

After a dilation with center (0, 0) the image of DB is D'B'. If DB = 4.5 and D'B' = 18, the scale factor of this dilation is

a)

1/5

b)

5

c)

1/4

d)

4

77.

On the graph below, point A(3, 4) and BC with coordinates B(4, 3) and C(2, 1) are graphed. What are the coordinates of B' and C' after BC undergoes a dilation centered at point A with a scale factor of 2?

a)

B'(5,2) and C'(1, -2)

b)

B'(6, 1) and C'(0, -1)

c)

B'(5, 0) and C'(1, -2)

d)

B'(5, 2) and C'(3, 0)

78.
How many degrees was the figure rotated?
a)
90 degrees counterclockwise 
b)
180 degrees
c)
270 counterclockwise 
d)
90 degrees clockwise
79.
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.
80.
What Transformation is visible?
a)
Reflection
b)
Translation
c)
Rotation
d)
Dilation
81.
Triangle ABC has vertices A(-4, 1), B(-2, 1), and C(-1, -2) on a coordinate grid. If ∆ABC is rotated 180° about the origin, what are the coordinates of A'B'C'?
a)
A'(1,4) B'(1,2) C'(-2,1)
b)
A'(4,-1) B'(2,-1) C'(1,2)
c)
A'(-1,-4) B'(-1,-2) C'(2,-1)
d)
A'(-4,1) B'(-2,1) C'(-1,-2)
82.
An office supply store sells index cards in two different sizes. The large size is a dilation of the small size. Both sizes are shown. Find the scale factor of the dilation.
a)
0.5
b)
5
c)
3
d)
⅓
83.

What is the rule for rotating a figure 90 degrees counterclockwise

a)

(-y, x)

b)

(-x, -y)

c)

(y, -x)

d)

(-y, -x)

84.

What is the rule for rotating a figure 180 degrees

a)

(-y, x)

b)

(-x, -y)

c)

(y, -x)

d)

(-y, -x)

85.

What is the rule for rotating a figure 270 degrees counterclockwise

a)

(-y, x)

b)

(-x, -y)

c)

(y, -x)

d)

(-y, -x)

86.
Rotate the point (5,5) around the origin 180 degrees. State the image of the point.
a)
(5,-5)
b)
(5,5)
c)
(-5,5)
d)
(-5,-5)
87.
If you were to rotate ABCD 180°  about the origin, what would the coordinate of A' be?
a)
(-5, 5)
b)
(-3, -5)
c)
(-5, 3)
d)
(-3, 3)
88.
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)
89.
A turn is also called a ___________.
a)
Translation
b)
Reflection
c)
Rotation
d)
Transformation
90.
Reflection or Rotation
a)
Reflection
b)
Rotation
91.

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)

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