Question

HELP ME Write and solve a proportion to find y.

Answer 1

Given:

A figure of dilation and the center of dilation is O.

To find:

The value of y.

Solution:

The distance between center and vertex of image (d') is proportional to the distance between center and the corresponding vertex of original figure (d).

`d'\propto d`

`d'=kd`

`(d')/(d)=k`

Where, k is the scale factor or constant of proportionality.

So, the scale factor for the given dilation is

`k=(OB')/(OB)`

`k=(36)/(16)`

`k=(9)/(4)`

We know that,

`k=\frac{\text{Side length of image}}{\text{Corresponding side length of original figure}}`

`(9)/(4)=(A'C')/(AC)`

`(9)/(4)=(27)/(y)`

`9* y=27* 4`

Divide both sides by 9.

`y=(27* 4)/(9)`

`y=3* 4`

`y=12`

Therefore, the value of y is 12.