Question

Line segment XY is dilated to create line segment X'Y' using point T as the center of dilation.

Answer 1

Answer:

$YT=12\ units$

Step-by-step explanation:

we know that

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

Triangles XYT and X'Y'T are similar by AA Similarity Theorem

so

$\frac{XT}{YT}=\frac{X'T}{Y'T}$

substitute the given values

$\frac{8}{YT}=\frac{6}{9}$

$YT=9(8)/6\\YT=12\ units$