Question

dilate figure ( pqrs ) by a scale factor of ( \frac{1}{2} ) with the center of dilation at point ( p ).
to dilate the figure, think about the lengths of the corresponding sides.
what is the length of ( pq ), the image of segment ( pq )?
( pq= ) units

Explanation:

Step1: Find the length of \(PQ\)

Count the units between \(P\) and \(Q\) on the grid. \(PQ = 14\) units.

Step2: Apply the dilation formula

The formula for dilation is \(PQ'=k\times PQ\), where \(k = \frac{1}{2}\) (scale factor).
Substitute \(PQ = 14\) and \(k=\frac{1}{2}\) into the formula: \(PQ'=\frac{1}{2}\times14\).
Calculate \(\frac{1}{2}\times14 = 7\).

Answer:

\(7\)