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Dilations Review

Total questions: 80

Worksheet time: 6hrs 59mins

Name
Class
Date
1.

Match the terms with their definitions.

a)

Translation

1.

A transformation that slides a figure.

b)

Rotation

2.

A transformation that turns a figure around a point.

c)

Reflection

3.

A transformation that flips a figure across a line.

d)

Dilation

4.

A transformation that makes a scale copy

2.

Two figures are congruent if they have the _______ shape and _______ size.

a)
Different, Same
b)
Same, Same
c)
Same, Different
d)
Different, Different
3.

Two figures can be similar if they have the _______ shape but _______ size.

a)
Different, Same
b)
Same, Same
c)
Same, Different
d)
Different, Different
4.

What symbol is used to show that two figures are similar?

a)

\sim

b)

c)

d)

=

5.
When a dilation has a scale factor greater than one, the dilation is an enlargement.
a)
True
b)
False
6.

When the scale factor of a dilation is between 0 and 1, the dilation is a reduction (shrinks).

a)
True
b)
False
7.

Point B (-10,-6) is dilated with a scale factor of 1/2 and the center of dilation at the origin. What are the coordinated of B'?

a)
(5,3)
b)
(20,12)
c)
(-20,-12)
d)
(-5,-3)
8.

Figure DMPN is dilated to form figure D'M'P'N. What is the scale factor?

a)
2
b)
3
c)
1/3
d)
1/2
9.
The point (8, 12) was dilated to become point (2, 3). What was the scale factor?
a)
½
b)
¼
c)
4
d)
2
10.

Triangle ABC is dilated using a scale factor of 1/2. The center of dilation is at the origin. What are the new coordinates of point A'?

a)
(-3, 3)
b)
(-12, 12)
c)
(-2, 2)
11.

The points of Δabc\Delta abc is graphed. The figure is dilated with a scale factor of 2 and the center of dilation at the origin. Plot all the points of Δabc\Delta a'b'c' after performing the dilation.

12.

The vertices of △ ABC are located at A(4,8), B(8,0), and C(-8,4). Which sequence of transformations of △ ABC results in △ A′′B′′C′′?

a)

Rotate △ ABC 90° clockwise around the origin. Dilate the image by a scale factor of 4 with a center of dilation at the origin.

b)

Rotate △ ABC 90° counterclockwise around the origin. Dilate the image by a scale factor of 4 with a center of dilation at the origin.

c)

Rotate △ ABC 90° clockwise around the origin. Dilate the image by a scale factor of 1/4 with a center of dilation at the origin.

d)

Rotate △ ABC 90° counterclockwise around the origin. Dilate the image by a scale factor of 1/4 with a center of dilation at the origin.

13.

Finish the following similarity statement: Figure DEFGHI ∼ Figure ​ (a)  

Choose from the below words
DEFGHI
D'E'F'G'H'I'
ABCDEF
A'B'C'D'E'F'
14.

Figures A, B, C, and D are drawn. The center of dilation is point E. Which of the following figures are similar to figure A? Choose all correct answers.

a)

Figure B

b)

Figure C

c)

Figure D

15.

Triangle EFG is drawn on the coordinate plane. The triangle is dilated by a scale factor of 1/3, with the center of dilation at the origin, to form triangle E'F'G'. Then, triangle E'F'G' is translated 3 units to the right to form triangle E''F''G''. What is the coordinate of E'' ?

(a)  

16.
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
17.
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.
18.
Definition: The figure before a transformation has occurred. 
a)
Pre-image
b)
Image
c)
Translation
d)
Reflection
19.
Definition: The figure after a transformation has occurred. 
a)
Pre-image
b)
Image
c)
Translation
d)
Reflection
20.
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
21.
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)
22.
Does the image show a dilation?
a)
Yes
b)
No
23.
Does the image show a Dilation?
a)
Yes
b)
No
24.
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)
25.
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)
26.
a)
1/2
b)
3/2
c)
2
d)
1
27.
a)
(-2,-2)
b)
(0,0)
c)
(1,1)
d)
(-2,-1)
28.
Dilate Point A by a scale factor of 1/2
a)
(-4,-4)
b)
(-1,-4)
c)
(-1,-1)
d)
(-2,-2)
29.
Choose the correct scale factor:
a)
2.5
b)
1.5
c)
3.5
d)
4
30.
Choose the correct scale factor:
a)
2
b)
3
c)
1/3
d)
1/2
31.
(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 : ( 
32.
What is the value of X?
a)
X=4
b)
X=6
c)
X=3
d)
X=2
33.
Are the triangles similar?
a)
Yes
b)
No
34.
Are the triangles similar?
a)
Yes
b)
No
35.
Similarity Ratio: _
a)
2/3
b)
1/2
c)
2
d)
3
36.
When you dilate a figure you...
a)
slide it.
b)
turn it.
c)
flip it.
d)
make it larger or smaller.
37.
All corresponding angles are congruent in similar figures.
a)
True
b)
False
38.
All corresponding sides are proportional (same ratio) in similar figures.
a)
True
b)
False
39.
Find x
a)
21
b)
27/7
c)
13
d)
18
40.
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.
41.
What is the height of the Tree?
a)
20
b)
15
c)
30
d)
10
42.
If two figures are similar their angles are______.
a)
proportional
b)
congruent
c)
supplementary
d)
complementary
43.
If two figures are similar, the corresponding sides are ______________.
a)
equal
b)
congruent
c)
proportional
d)
none of these
44.
What happens to a figure when it is dilated by a scale factor of a positive integer?
a)
it becomes smaller
b)
it becomes larger
c)
it stays the same
45.
What happens to a figure when it is dilated by a scale factor of a fraction less than 1?
a)
it becomes smaller
b)
it becomes larger
c)
it stays the same
46.

Jimmy and his sister each bought a plot of rectangular land to build a house. Jimmy's land was 150 ft by 100 ft. His sister's land was 75 ft by 50 ft. What is the scale factor of Jimmy's land compared to his sister's?

a)

1/2 the size

b)

2 times the size

c)

2/3 the size

d)

3 times the size

47.
Susie and Emily are each going to paint a mural on their bedroom wall.  Susie uses up most of the wall for her mural of the solar system.  It turns out to be 10 ft by 12 ft of wall space. Emily paints a small picture of a cow grazing in the field.  It only takes up one-fifth of the amount of wall space Susie used.  What are the dimensions of Emily's mural?
a)
50 feet by 60 feet
b)
5 feet by 6 feet
c)
2 feet by 2.4 feet
d)
20 feet by 24 feet
48.
What is the algebraic rule for the dilated image?
a)
( x , y ) --> ( 3x, 3y )
b)
( 3x, 3y ) --> ( x , y )
c)
(x , y) --> (0.3x , 0.3y)
d)
( x , y ) --> ( 2x, 2y )
49.
Choose the correct scale factor:
a)
2
b)
3
c)
1/3
d)
1/2
50.

Which of the following rules represents a dilation?

a)

(x, y) → (x, 3y)

b)

(x, y) → (3x, 3y)

c)

(x, y) → (x - 4, y - 3)

d)

(x, y) → (.5x, .4y)

51.
The point (8, 12) was dilated to become point (2, 3). What was the scale factor?
a)
½
b)
¼
c)
4
d)
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.
Similar figures have the same ______ but different ______. 
a)
measure; shapes
b)
sizes; shapes
c)
value; measures
d)
shape; sizes
54.
In a dilation what mathematical operation is used with the scale factor?
a)
addition 
b)
subtraction 
c)
multiplication 
d)
division 
55.
Triangle ABC is dilated using the algebraic rule (x, y) --> (0.75x, 0.75y). Is triangle A'B'C' an enlargement or reduction of the original triangle?
a)
Enlargement because the scale factor is less than one. 
b)
Reduction because the scale factor is less than one. 
c)
Neither
d)
Cannot Be Determined
56.
Using the algebraic rule (x, y) --> (2.5x, 2.5y), what would be the coordinates of C' if point C is located at (-10, 8).
a)
C'(-4, 3.2)
b)
C'(-25, 20)
c)
C'(-25, 8)
d)
C'(-4, 20)
57.
What is the algebraic rule for the dilated image? 
a)
(x, y) --> (2x, 2y)
b)
(2x, 2y) --> (x, y)
c)
(x, y) --> (0.5x, 0.5y)
d)
(x, y) --> (x+1, y+2)
58.

What angle is corresponding to angle D?

a)

A

b)

B

c)

C

d)

F

59.

If ABCDE is similar to LMNOP, which proportion is NOT true?

a)
b)
c)
d)
60.

If ABCD is similar to EFGH, which proportion is true?

a)
b)
c)
d)
61.

Select ALL the true statements about an image after a dilation.

a)

The image is a different shape than the preimage.

b)

The image is a different size than the preimage.

c)

The image has the same angle measures as the preimage.

d)

The image is similar to the preimage.

e)

The image has the same side lengths as the preimage.

62.

Triangle PQR is the image of triangle JKL after a dilation. Is the dilation an enlargement or a reduction? Explain.

a)

Enlargement, because the image is larger than the original figure.

b)

Enlargement, because the image is smaller than the original figure.

c)

Reduction, because the image is smaller than the original figure.

d)

Reduction, because the image is larger than the original figure.

63.

Rajesh is making pennants in preparation for a school soccer game. He wants the pennants to be similar triangles. Which of these triangles could he use for the pennants?

a)

QRS and TVW

b)

QRS and XYZ

c)

TVW and JKL

d)

TVW and XYZ

64.

Are ABC and DEF similar?

a)

Yes

b)

No

65.

Are ABC and LMN similar?

a)

Yes

b)

No

66.

Are LMN and DEF similar?

a)

Yes

b)

No

67.

Figure D´E´F´G´ is a dilation with center (0, 0) of figure DEFG. What is the scale factor?

(a)  

68.

A sequence of transformations is required to map ΔPQR onto ΔP’Q’R’. Which is a possible step?

a)

A dilation with scale factor 1

b)

A dilation with scale factor 2

c)

A dilation with scale factor 3

d)

A dilation with scale factor 4

69.

Find the image of ΔABC after a dilation with center (0, 0) and a scale factor of 3. What is the ordered pair for A'?

a)

(1, 1)

b)

(3, 3)

c)

(5, 5)

d)

(6, 6)

70.

Triangle DEF is similar to triangle ABC. What is a sequence of transformations that maps triangle ABC to triangle DEF?

a)

Reflection then rotation

b)

Rotation then dilation with scale factor of 2

c)

Rotation then dilation with scale factor of 0.5

d)

Rotation then translation

71.

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

72.

A dilation always produces a congruent figure.

a)

True

b)

False

73.

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

74.

Did the image enlarge, reduce or none of the above?

a)

Enlarge

b)

Reduce

c)

None of the above

75.

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

76.

Under a dilation, which scale factor will result in a congruent image?

a)

-2

b)

0

c)

1

d)

1/2

77.

An image is dilated at a scale factor of 1.5. This means the dilation is an enlargement and the dilated image will be bigger.

a)

True

b)

False

78.

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

Choose from the below words
(x, y) → (x, 3y)
(x, y) → (3x, 3y)
(x, y) → (x, y - 3)
(x, y) → (.5x, .4y)
79.

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
80.

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

Type in a whole number, decimal or fraction.