Question

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

Answer 1

The answer 

X'Y' and XY are parallels, measX'Y'T = measXYT, there is similarity between the two triangles, we can find YT by using theorem of thales, 

it is TY' / TY =TX' / TX =X'Y' /XY, so TY' / TY = TX' / TX = 9/ TY =6/ 2+6=6/8

and then 9/ TY = 6/8 therefore  TY= 12

Answer 2

yeah ,the answer is c on edg