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 = \frac{1}{2} \cdot pq\\) \\(pq = \boxed{12}\\) units

Explanation:

Step1: Determine length of PQ

From the grid, count the units between P and Q. Let's assume PQ is 12 units (as per the formula hint).

Step2: Apply dilation formula

The formula for the length of the dilated segment \( PQ' \) is \( PQ' = \frac{1}{2} \cdot PQ \). Substituting \( PQ = 12 \) into the formula, we get \( PQ' = \frac{1}{2} \times 12 \).

Step3: Calculate the result

\( \frac{1}{2} \times 12 = 6 \).

Answer:

6