Question

dilate figure pqrs by a scale factor of \\( \frac { 1 } { 2 } \\) with the center of dilation at point p.
\\( p q ^ { prime } = \\) units
\\( s ^ { prime } p = \\) units
what is the length of \\( r ^ { prime } s ^ { prime } \\), the image
of segment \\( r s \\) ?
\\( r ^ { prime } s ^ { prime } = \\) units

Explanation:

Step1: Determine the length of segment \( RS \)

By counting the units on the grid, \( RS = 2 \) units.

Step2: Apply the dilation formula

The formula for dilation is \( \text{Length of image}=\text{Scale factor}\times\text{Length of original segment}\).
Given scale factor \( k=\frac{1}{2} \) and original length \( RS = 2 \) units.
So, \( R'S'=k\times RS=\frac{1}{2}\times2\)

Answer:

\(1\)