Question

The area of a rectangle is 100cm2. After a dilation, the area is 25cm2. What is the scale factor?

Answer 1

The scale factor is 1/2

Explanation:

we know that

A dilation is a non rigid transformation that produces similar figures

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

Let

z ---> the scale factor

x ---> the area after dilation

y ---> the original area

`z^2=(x)/(y)`

we have

`x=25\ cm^2\\y=100\ cm^2`

substitute

`z^2=(25)/(100)`

`z^2=(1)/(4)`

`z=(1)/(2)`