Question

1. the triangle abc is taken to triangle abc by a dilation. select all of the scale factors for the dilation that would result in an image that was smaller than the original figure.

a. \\(\frac{1}{2}\\) b. \\(\frac{8}{9}\\)
c. 1 d. \\(\frac{3}{2}\\)
e. 2

Explanation:

Step1: Recall dilation scale factor rule

For a dilation, if the scale factor \( k \) satisfies \( 0 < k < 1 \), the image is smaller than the original figure. If \( k = 1 \), the image is congruent. If \( k>1 \), the image is larger.

Step2: Analyze each option

• Option A: \( \frac{1}{2} \). Since \( 0<\frac{1}{2}<1 \), this scale factor will make the image smaller.
• Option B: \( \frac{8}{9} \). Since \( 0 < \frac{8}{9}< 1 \) (because \( 8 < 9 \)), this scale factor will make the image smaller.
• Option C: \( 1 \). A scale factor of 1 means the image is congruent (same size), not smaller.
• Option D: \( \frac{3}{2} \). Since \( \frac{3}{2}=1.5>1 \), this scale factor will make the image larger.
• Option E: \( 2 \). Since \( 2 > 1 \), this scale factor will make the image larger.

Answer:

A. \(\frac{1}{2}\), B. \(\frac{8}{9}\)