Question

1. identify the scale factor if prq is dilated onto sut. state whether it is an enlargement or reduction. show your work!!!

(images of triangles prq and sut with side lengths: prq has pr=8, rq=6, pq=10; sut has su=12, ut=9, st=15)

Explanation:

Step1: Find corresponding sides

Triangle \( PRQ \) has sides \( PR = 8 \), \( RQ = 6 \), \( PQ = 10 \). Triangle \( SUT \) has sides \( SU = 12 \), \( UT = 9 \), \( ST = 15 \).

Step2: Calculate scale factor

Scale factor \( k=\frac{\text{Length of side in } SUT}{\text{Length of corresponding side in } PRQ} \). For \( PR \) and \( SU \): \( k = \frac{12}{8}=\frac{3}{2}=1.5 \). Check with other sides: \( \frac{9}{6}=1.5 \), \( \frac{15}{10}=1.5 \).

Step3: Determine enlargement/reduction

Since \( k = 1.5>1 \), it is an enlargement.

Answer:

The scale factor is \( \frac{3}{2} \) (or \( 1.5 \)) and it is an enlargement.