Question

Figure 1 is dilated to get Figure 2.

What is the scale factor?


Enter your answer in simplest form in the box. ___

Answer 1

The scale factor is 5/8

Answer 2

`\text{Scale factor}=(5)/(8)`

Explanation:

We have been given an image of two pentagons and we are asked to find the scale factor of dilation.

Since the corresponding sides of pre-image are proportional to the corresponding sides of image after dilation, so we can find the scale fctor for the given dilation as:

`\text{Pre-image}* \text{Scale factor}=\text{ Image after dilation}`

Upon substituting the given lengths of corresponding sides we will get,

`16 * \text{Scale factor}=10`

Dividing both sides by 16 we will get,

`\frac{16 * \text{Scale factor}}{16}=(10)/(16)`

`\text{Scale factor}=(2*5)/(2*8)`

`\text{Scale factor}=(5)/(8)`

Therefore, the scale factor of given dilation is
`(5)/(8)`.