Question

In the diagram below, triangle RST is the image of triangle MAP after a dilation of scale factor k with center E. Which ratio is equal to scale factor k of dilation?

Please use the photo and please explain how you got the answer step by step, thanks

Answer 1

The scale factor is equal to 2

Explanation:

we know that

Triangle RST is the image of Triangle MAP after a dilation

That means

The dilation is an enlargement

Remember that

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

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

Let

z ----> the scale factor

`z=(TS)/(PA)=(TR)/(PM)=(RS)/(MA)`

Find the length of the segment TR and PM

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

`d=\sqrt{(y2-y1)^(2)+(x2-x1)^(2)}`

step 1

Find the distance TR

we have

T(-11,8) and R(-9,0)

substitute in the formula

`d=\sqrt{(0-8)^(2)+(-9+11)^(2)}`

`d=\sqrt{(-8)^(2)+(2)^(2)}`

`d_T_R=√(68)\ units`

step 2

Find the distance PM

we have

P(-5,4) and M(-4,0)

substitute in the formula

`d=\sqrt{(0-4)^(2)+(-4+5)^(2)}`

`d=\sqrt{(-4)^(2)+(1)^(2)}`

`d_P_M=√(17)\ units`

step 3

Find the scale factor

`z=(TR)/(PM)`

we have

`d_T_R=√(68)\ units`

`d_P_M=√(17)\ units`

substitute

`z=(√(68))/(√(17))=2`

therefore

The scale factor is equal to 2