Question

line segment xy is dilated to create line segment xy using point t as the center of dilation. what is yt? x 2 x 6 t y 9 y 3 units 6 units 12 units 15 units

Explanation:

Step1: Find dilation scale factor

Scale factor $k = \frac{X'T}{XT} = \frac{6}{2+6} = \frac{6}{8} = \frac{3}{4}$? No, wait: $XT = XX' + X'T = 2 + 6 = 8$, $X'T = 6$, so $k = \frac{X'Y'}{XY} = \frac{T Y'}{T Y} = \frac{6}{8} = \frac{3}{4}$? Wait, $T Y' = 9$, so let $T Y = x$, then $\frac{3}{4} = \frac{9}{x} \Rightarrow x = 12$.

Step2: Confirm TY value

Since $TY' = 9$ and scale factor $\frac{3}{4} = \frac{TY'}{TY}$, solving $\frac{3}{4} = \frac{9}{TY}$ gives $TY = 12$.

Answer:

C. 12 units