Under a dialation, triangle A(0,0) B(0,4) C(6,0) becomes triangle A'(0,0) B'(0,10) C'(15,0). what is the scale factor for this dialation

The scale factor is 2.5

Step-by-step explanation:

we know that

A 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

Let

z ---> the scale factor

so

the formula to calculate the distance between two points is equal to

step 1

Find the distance AB

we have

A(0,0) B(0,4)

substitute

step 2

Find the distance A'B'

we have

A'(0,0) B'(0,10)

substitute

step 3

Find the scale factor

substitute the values

therefore

The scale factor is 2.5 ( is an enlargement)