Line segment XY is dilated to create line segment X'Y' using point T as the center of dilation.
Point T is the center of dilation. Line segment X Y is dilated to create shorter line segment X prime Y prime. The length of T X prime is 6 and the length of T Y prime is 9. The length of X X prime is 2.
What is YT?
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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
substitute the given values