The length of segment YT will be equal to 12 units as the line segment XY is dilated to create line segment X'Y' using point t as the center of dilation.
Dilation means changing the size of an object without changing its shape. The size of the object may be increased or decreased based on the scale factor.
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 to the AA Similarity Theorem
[tex]\dfrac{XT}{YT}=\dfrac{X'T}{Y'T}[/tex]
substitute the given values
[tex]\dfrac{8}{YT}=\dfrac{6}{9}[/tex]
[tex]YT=\dfrac{9\times 8}{6}[/tex]
[tex]YT=12\ units[/tex]
Hence the length of segment YT will be equal to 12 units as the line segment XY is dilated to create line segment X'Y' using point t as the center of dilation.
To know more about dilation follow
https://brainly.com/question/10253650
