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 dilation formula

The formula for dilation is \(PG'=\text{scale factor}\times PG\). Let the scale factor \(k = \frac{1}{6}\), and \(PG'\) is given as \(0.5\) units. We need to solve for \(PG\).

Step2: Rearrange the formula to solve for \(PG\)

From \(PG'=k\times PG\), we can get \(PG=\frac{PG'}{k}\).

Step3: Substitute the values

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

Step4: Calculate the result

\(0.5\times6 = 3\)

Answer:

3 units