Question

triangle abc is a dilation of triangle abc. the scale factor is
\frac{2}{3}. point b is 11 inches away from the center of dilation.
how far away from the center of dilation is point b?

22 inches

33 inches

\frac{3}{22} inches

\frac{22}{3} inches

Explanation:

Step1: Recall the formula for dilation

The distance from the center of dilation for a point \(P'\) (image) and \(P\) (pre - image) is given by \(d(P',O)=k\times d(P,O)\), where \(k\) is the scale factor and \(O\) is the center of dilation.

Step2: Substitute the given values

We know that \(k = \frac{2}{3}\) and \(d(B,O)=11\) inches. Then \(d(B',O)=k\times d(B,O)\).
Substitute \(k=\frac{2}{3}\) and \(d(B,O) = 11\) into the formula: \(d(B',O)=\frac{2}{3}\times11=\frac{22}{3}\) inches.

Answer:

\(\frac{22}{3}\) inches (the fourth option)