Question

Pre image ABCD was dilated to be image A’B’C’D, where the center of dilation is the origin. What scale factor was used in the dilation

Answer 1

The scale factor is 0.25

Explanation:

we know that

The dilation is a non-rigid transformation that produce similar figures

If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor

In this problem

ABCD and A'B'C'D' are similar

therefore

`(A'B')/(AB)=(B'C')/(BC)=(C'D')/(CD)=(A'D')/(AD)`

Find the scale factor

Looking at the graph

we have

`A'B'=1\ unit\\AB=4\ units`

Let

z ---> the scale factor

`z=(A'B')/(AB)`

substitute the values

`z=(1')/(4)=0.25`