Question

ii. what is the scale factor, if qrs is a dilation of prt?

Explanation:

Step1: Find the length of \( PR \)

Since \( PR=RQ + QP \), and \( RQ = 3.9 \), \( QP=1.1 \), then \( PR=3.9 + 1.1=5 \)

Step2: Find the length of \( RT \)

Since \( RT=RS + ST \), and \( RS = 4.8 \), \( ST=1.4 \), then \( RT=4.8+1.4 = 6.2 \)

Step3: Determine the scale factor

The scale factor \( k\) of dilation from \( \triangle PRT\) to \( \triangle QRS\) is calculated by the ratio of corresponding sides. Let's use \( \frac{RQ}{PR}\) (or we can use other pairs of corresponding sides). \( k=\frac{RQ}{PR}\), substituting \( RQ = 3.9\) and \( PR = 5\), we get \( k=\frac{3.9}{5}=0.78\)

Answer:

The scale factor is \( 0.78 \)