Question

the scale factor of the dilation of segment hg is $\frac{1}{6}$. if pg equals 0.5 units, what is pg? 2.5 units 3 units 4.5 units 6 units

Explanation:

Step1: Recall the formula for scale factor

The scale factor \(k=\frac{PG'}{PG}\). Given \(k = \frac{1}{6}\) and \(PG'=0.5\) units.

Step2: Solve for \(PG\)

From \(k=\frac{PG'}{PG}\), we can rewrite it as \(PG=\frac{PG'}{k}\). Substitute \(PG' = 0.5\) and \(k=\frac{1}{6}\) into the formula. Then \(PG=\frac{0.5}{\frac{1}{6}}\). Using the rule \(\frac{a}{\frac{b}{c}}=a\times\frac{c}{b}\), we have \(PG = 0.5\times6\).

Answer:

\(3\) units. So the answer is \(3\) units.