Question

select all scale factors that would dilate triangle qrs so that its image, triangle qrs, is smaller. a (triangle qrs with side lengths 7, 3, 6) options: 1, 0.5, 5/4, 0.75, 1/3

Explanation:

Step1: Recall dilation scale factor rule

A dilation with scale factor \( k \) makes the image smaller if \( 0 < k < 1 \), same size if \( k = 1 \), and larger if \( k>1 \).

Step2: Analyze each option

• For \( k = 1 \): \( 1 = 1 \), so image is same size, not smaller.
• For \( k = 0.5 \): \( 0 < 0.5 < 1 \), so image is smaller.
• For \( k=\frac{5}{4}=1.25 \): \( 1.25>1 \), so image is larger.
• For \( k = 0.75 \): \( 0 < 0.75 < 1 \), so image is smaller.
• For \( k=\frac{1}{3}\approx0.333 \): \( 0 < \frac{1}{3} < 1 \), so image is smaller.

Answer:

0.5, 0.75, 1/3 (the checkboxes for 0.5, 0.75, and 1/3 should be selected)