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Similarity Transformation Worksheet

Similarity Transformation Worksheet
  • Page 1
 1.  
Find the scale factor of dilation of the triangle ABC to the triangle AED.


a.
2
b.
2.5
c.
6.25
d.
1 2


Solution:

Scale factor = AE / AB

= 20 / 8 = 5 / 2 = 2.5
[Substitute the values and simplify.]

So, the scale factor is 2.5.


Correct answer : (2)
 2.  
Find the scale factor of dilation of the rectangle ABCD to the rectangle AEFG.


a.
5
b.
5 3
c.
2.5
d.
3


Solution:

Scale factor = AB / AE

= 50 / 10 = 5
[Substitute the values and simplify.]

So, the scale factor is 5.


Correct answer : (1)
 3.  
Find the scale factor for the dilation.

a.
3 4
b.
3 2
c.
4 5
d.
2 3


Solution:

Scale factor = New lengthOriginal length

= 22.50 / 15 = 1.5 = 3 / 2
[Substitute the values and simplify.]

So, the scale factor is 3 / 2.


Correct answer : (2)
 4.  
Find the scale factor for the dilation.

a.
2.5
b.
6.5
c.
3
d.
2


Solution:

Scale factor = New lengthOriginal length

= 24 / 9.6 = 2.5
[Substitute the values and simplify.]

So, the scale factor is 2.5.


Correct answer : (1)
 5.  
Find the length of the base of the new triangle after reduction by a scale factor of 1 4.

a.
24 in.
b.
12 in.
c.
48 in.
d.
3 in.


Solution:

Length of the base of the new triangle = Length of the base of the old triangle × scale factor

= 12 × 14 = 3
[Substitute the values and simplify.]

So, length of the base of the new triangle is 3 inches.


Correct answer : (4)
 6.  
A′B′C′D′ is a dilation of ABCD. Find the scale factor.

a.
2
b.
1 3
c.
3 2
d.
2 3


Solution:

To find the scale factor, we divide the length of one side of the dilated figure by the length of the corresponding side of the original figure.

Scale factor = A'D'AD

= A'D'BC
[AD = BC.]

= 128 = 3 / 2


Correct answer : (3)
 7.  
A parking lot is in the shape of a square measuring 19 ft by 12 ft. If you extend it by a scale factor of 3.5, find the new area of the parking lot.
a.
2793 ft2
b.
228 ft2
c.
235 ft2
d.
798 ft2


Solution:

New area of the parking lot = Area of the original parking lot × (scale factor)2
[Increasing the length of a side of an object by factor x increases the area by factor x2 .]

= (19 × 12) × (3.5)2

= 2793 ft2

Therefore, the new area of the parking lot is 2793 ft2.


Correct answer : (1)
 8.  
Square ABCD is dilated by a scale factor of 2 with the center of dilation at (0, 0). What will be the area of the new square?

a.
It is 4 times the area of square ABCD.
b.
It is 2 times the area of square ABCD.
c.
It is 1 4 the area of square ABCD.
d.
It is 1 2 the area of square ABCD.


Solution:

New area of the square A′B′C′D′ = Area of the square ABCD × (scale factor)2
[Increasing the length of a side of an object by factor x increases the area by factor x2.]

= Area of the square ABCD × (2)2

= 4 × Area of the square ABCD

Therefore, the area of new square will be 4 times the area of square ABCD.


Correct answer : (1)
 9.  
A triangle of base 5 cm is enlarged to have a base of 8 cm. Find the scale factor.
a.
5
b.
5 8
c.
8
d.
8 5


Solution:

Scale factor of a dilation describes the size of the change from the original figure to its image.

= 85

Therefore, the scale factor is 8 / 5.


Correct answer : (4)
 10.  
The length of a rectangle PQRS is 15 m. Find the measure of the dilation image for a scale factor of 4 5.
a.
12 m
b.
15 m
c.
7 m
d.
18.75 m


Solution:

Length of the rectangle = 15 m

Scale factor = 4 / 5

Measure of the dilation image = length of the rectangle × scale factor

= 15 × 4 / 5 = 12 m

Therefore, the measure of the dilation image is 12 m.


Correct answer : (1)

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