Answer:
The scale factor is equal to 2
Step-by-step 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
[tex]z=\frac{TS}{PA}=\frac{TR}{PM}=\frac{RS}{MA}[/tex]
Find the length of the segment TR and PM
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
step 1
Find the distance TR
we have
T(-11,8) and R(-9,0)
substitute in the formula
[tex]d=\sqrt{(0-8)^{2}+(-9+11)^{2}}[/tex]
[tex]d=\sqrt{(-8)^{2}+(2)^{2}}[/tex]
[tex]d_T_R=\sqrt{68}\ units[/tex]
step 2
Find the distance PM
we have
P(-5,4) and M(-4,0)
substitute in the formula
[tex]d=\sqrt{(0-4)^{2}+(-4+5)^{2}}[/tex]
[tex]d=\sqrt{(-4)^{2}+(1)^{2}}[/tex]
[tex]d_P_M=\sqrt{17}\ units[/tex]
step 3
Find the scale factor
[tex]z=\frac{TR}{PM}[/tex]
we have
[tex]d_T_R=\sqrt{68}\ units[/tex]
[tex]d_P_M=\sqrt{17}\ units[/tex]
substitute
[tex]z=\frac{\sqrt{68}}{\sqrt{17}}=2[/tex]
therefore
The scale factor is equal to 2
