Question

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

Explanation:

Step1: Use the property of dilation

For a dilation with center \(T\), \(\frac{XT}{X'T}=\frac{YT}{Y'T}\). Let \(YT = x\). We know \(XT=2 + 6=8\), \(X'T = 6\), and \(Y'T=9\).

Step2: Set up the proportion

\(\frac{8}{6}=\frac{x}{9}\) (by the similarity of triangles formed by the dilation, since corresponding sides of similar figures are proportional).

Step3: Solve the proportion for \(x\)

Cross - multiply: \(6x=8\times9\). So \(6x = 72\). Then \(x=\frac{72}{6}=12\).

Answer:

12 units