Question

find the scale factor when pqrs is dilated to pqrs in the following figure.

two rectangles: smaller one pqrs with pq = 10 ft, larger one pqrs with pq = 30 ft

options: 3, 5, 0.3, 2

Explanation:

Step1: Recall Scale Factor Formula

The scale factor \( k \) for a dilation is given by \( k=\frac{\text{Length of image}}{\text{Length of original}} \).

Step2: Identify Corresponding Sides

For rectangles \( PQRS \) (original) and \( P'Q'R'S' \) (image), the length of \( PQ \) is \( 10 \) ft (original), and the length of \( P'Q' \) is \( 30 \) ft (image).

Step3: Calculate Scale Factor

Using the formula, \( k = \frac{30}{10}=3 \).

Answer:

3