Dilation Worksheet

Dilation Worksheet
  • Page 1
 1.  
Which of the following is/are correct?
1. Every dilation has a center.
2. Every dilation has a scale factor.
3. Every dilation increases the size of the picture.
4. Every dilation is a transformation.
a.
2, 3, and 4 only
b.
1, 2 and 4 only
c.
1, 2 and 3 only
d.
All are correct


Solution:

Every dilation has a center and a scale factor.

Every dilation is a transformation.

A dilation can either increase or decrease the size of the original picture.

Statements 1, 2 and 4 only are correct.


Correct answer : (2)
 2.  
Select the correct statement/ statements.
1. P is the center of dilation
2. Scale factor of the dilation x maps Q′ to Q
3. QQ′ = PQ (x - 1)


a.
All are correct
b.
2 and 3 only
c.
1 and 3 only
d.
1 and 2 only


Solution:

P is the center of dilation.

Scale factor of x maps Q to Q′ and not Q′ to Q.

QQ′ = PQ′ - PQ = x PQ - PQ = PQ (x - 1)

Statements 1 and 3 only are correct.


Correct answer : (3)
 3.  
What is the scale factor that maps square ABCD to square AEFG?
[Given a = 2 and b = 10.]


a.
6
b.
12
c.
5
d.
1 5


Solution:

Scale factor = AE / AB

= 2+102

= 12 / 2 = 6


Correct answer : (1)
 4.  
Find the scale factor that maps PQRS onto ABCD.

a.
1.5
b.
3
c.
2
d.
0.5


Solution:

Scale factor = DA / SP

= 3 / 6

= 0.5


Correct answer : (4)
 5.  
Find the image of point P (3, 4) under dilation with center (0, 0) with a scale factor of 2.
a.
(- 3, - 4)
b.
(6, 8)
c.
(- 6, 8)
d.
(6, - 8)


Solution:

To find the image of a point on the coordinate plane under dilation with center as origin, multiply the coordinates with scale factor.

Image of P (3, 4) is P ′(3 × 2, 4 × 2)

= (6, 8)


Correct answer : (2)
 6.  
Find the image of M(- 6, 12) under dilation with center as origin and with a scale factor of 56.
a.
(- 5, 10)
b.
(- 7, 14)
c.
(5 , - 10)
d.
(7, - 14)


Solution:

To find the image of a point on the coordinate plane under a dilation with center as origin, multiply the coordinates with the scale factor.

Image of M(- 6, 12) = (- 6 × 5 / 6, 12 × 5 / 6)

= (- 5, 10)


Correct answer : (1)
 7.  
Find the point of the image of point A after a dilation with center at the origin and scale factor of 2.5.


a.
R
b.
P
c.
Q
d.
M


Solution:

Point A is (- 4, 2).

When it is under dilation with a scale factor of 2.5, the image will be (- 4 × 2.5, 2 × 2.5) = (- 10, 5).

This point is shown as P in the picture.


Correct answer : (2)
 8.  
Find the scale factor when Q is dilated to P with center O.

a.
4
b.
1 4
c.
3
d.
1 3


Solution:

Q is (12, - 9).

P is (4, - 3).

The coordinates of P are 1 / 3 of those of Q.

Scale factor is 1 / 3.


Correct answer : (4)
 9.  
Select the dilated image of ABCD under a scale factor of 3.


a.
Neither figure 1 nor figure 2
b.
Figure 1
c.
Figure 2
d.
Both Figure 1 and Figure 2


Solution:

From the figures, the side AB is 3 times its original length both in figures 1 and 2.

But Figure 1, is not of the same shape of the original. Point C′ is not shown as dilated under a scale facor of 3. So, it is not a transformation.

Figure 2 is of similar size of that of the original. All the points are dilated under a scale factor of 3. It is a transformation.

Figure 2 is the dilation of ABCD under a scale factor of 3.


Correct answer : (3)
 10.  
Points A(1, 1) and B(9, 6) on an XY plane are dilated to A′ and B′ with the center as the origin. The scale factor of A is 4 and that of B is 1 3. Find the difference in the lengths between the line segments AB and A′ B′.


a.
63-13 units
b.
34 units
c.
89-5 units
d.
4 3units


Solution:

A and B are (1, 1) and (9, 6)
[Given.]

A′ = (4, 4)
[Multiply the coordinates by the scale factor.]

B′ = (3, 2)
[Multiply the coordinates by the scale factor.]

AB = [(9 - 1)² + (6 - 1)²]
[Distance formula.]

= 89
[Simplify.]

A′B′ = [(4 - 3)² + (4 - 2)²]
[Distance formula.]

A′B′ = 5
[Simplify.]

AB - A′B′ = 89-5 units
[Steps 5 and 7.]


Correct answer : (3)

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