# FIND SCALE FACTOR OF DILATION

In any enlargement or reduction, we multiply the lengths in the object by the scale factor to get the lengths in the image.

A scale factor is :

• greater than 1 for an enlargement
• less than 1 for a reduction

Using scale factor of

i) 2 and ii) 1/2

i) Since the scale factor is 2, it should be enlargement. To get enlarged figure, we have to multiply each side length by 2.

ii) Since the scale factor is 1/2, it should be reduction. To get reduced figure, we have to multiply each side length by 1/2.

In the following diagrams, A has been enlarged to A'. Find the scale factor.

Problem 1 :

Solution:

So, the scale factor is 2.

Because, the scale factor 2 is greater than 1, this is an enlargement.

Problem 2 :

Solution:

So, the scale factor is 3.

Because, the scale factor 3 is greater than 1, this is an enlargement.

Problem 3 :

Solution:

So, the scale factor is 1.5.

Because, the scale factor 1.5 is greater than 1, this is an enlargement.

In the following diagrams, B' is a reduction of B. Find the scale factor.

Problem 4 :

Solution:

So, the scale factor is 1/2.

Because the scale factor 1/2 is less than 1, this is a reduction.

Problem 5 :

Solution:

So, the scale factor is 1/6.

Because the scale factor 1/6 is less than 1, this is a reduction.

Problem 6 :

Solution:

So, the scale factor is 3/4.

Because the scale factor 3/4 is less than 1, this is a reduction.

In the following diagrams, A has been enlarged to B. Find the scale factor

Problem 7 :

Solution :

Calculating length of corresponding sides,

Length of the shape B = 4

Length of the shape A = 1

Scale factor = Dimension of shape B/Dimension of shape A

= 4/1

= 4

So, the scale factor is 4. It is enlargement.

Problem 8 :

Solution :

Calculating length of corresponding sides,

Length of the shape B = 4

Length of the shape A = 2

Scale factor = Dimension of shape B/Dimension of shape A

= 4/2

= 2

So, the scale factor is 2. It is enlargement.

Problem 9 :

Solution :

Calculating length of corresponding sides,

Length of the shape B = 2

Length of the shape A = 1

Scale factor = Dimension of shape B/Dimension of shape A

= 2/1

= 2

So, the scale factor is 2. It is enlargement.

Problem 10 :

Solution :

Calculating length of corresponding sides,

Length of the shape B = 1

Length of the shape A = 3

Scale factor = 1/3

So, the scale factor is 1/3. It is reduction.

Problem 11 :

Solution :

Calculating length of corresponding sides,

Length of the shape B = 1

Length of the shape A = 2

Scale factor = 1/2

So, the scale factor is 1/2. It is reduction.

Problem 12 :

Solution :

Calculating length of corresponding sides,

Length of the shape B = 1

Length of the shape A = 3

Scale factor = 1/3

So, the scale factor is 1/3. It is reduction.

Problem 13 :

Solution :

Calculating length of corresponding sides,

Length of the shape B = 3

Length of the shape A = 1

Scale factor = 3/1

So, the scale factor is 3. It is enlargement.

Problem 14 :

Solution :

Calculating length of corresponding sides,

Length of the shape B = 2

Length of the shape A = 1

Scale factor = 2/1

So, the scale factor is 2. It is enlargement.

Problem 15 :

Solution :

Calculating length of corresponding sides,

Length of the shape B = 1

Length of the shape A = 2

Scale factor = 1/2

So, the scale factor is 1/2. It is reduction

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