Question

The two figures are similar.

a) Write the similarity statement.
b) Is the image of the dilation a reduction or an enlargement of the original figure? Explain.
c) What is the scale factor? Explain.

Answer 1

Given:

Two similar figures.

Solution:

Part a:

ΔABC and ΔA'B'C' are similar.

Similarity statement:

If two triangles are similar, then the corresponding sides are in proportion.

`$(A B)/(A^(\prime) B^(\prime)) = (6)/(24) =(1)/(4)`

`$(BC)/(B^(\prime) C^(\prime)) = (12)/(48) =(1)/(4)`

`$(CA)/(C^(\prime) A^(\prime)) = (15)/(60) =(1)/(4)`

The sides are in the same ratio. Therefore the two triangles are similar.

Part b:

The sides of A'B'C' are greater than the original image ABC.

Therefore, the dilation A'B'C' is an enlargement.

Part c:

Scale factor:

`$K =\frac{\text {Side length of image }}{\text {Side length of original }}`

`$K =(A^(\prime)B^(\prime))/(AB)`

`$K =(24)/(6)`

K = 4

Scale factor = 4

K > 1

Therefore the image of the dilation is enlargement.