Question

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

Explanation:

Step1: Recall the dilation formula

The formula for dilation is \(A'B'=\text{scale factor}\times AB\). Here, if \(PQ'\) is the dilated segment and \(PQ\) is the original segment, and the scale factor \(k = \frac{1}{6}\), then \(PQ'=\frac{1}{6}PQ\).

Step2: Solve for \(PQ\)

We know that \(PQ' = 0.5\) units. From \(PQ'=\frac{1}{6}PQ\), we can rewrite it as \(PQ=6\times PQ'\).
Substitute \(PQ' = 0.5\) into the equation: \(PQ=6\times0.5\).

Answer:

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