Question

1. triangle abc is taken to triangle abc by a dilation. which of these scale factors for the dilation would result in an image that was larger than the original figure?

a
b
c
d

Explanation:

Step1: Recall Dilation Scale Factor

A dilation scale factor \( k \) determines the size of the image relative to the original. If \( k > 1 \), the image is larger; if \( 0 < k < 1 \), the image is smaller; if \( k = 1 \), the image is the same size.

Step2: Analyze Each Option

• Option a: \( \frac{1}{3} \) (less than 1, image smaller)
• Option b: \( \frac{11}{12} \) (less than 1, image smaller)
• Option c: \( 1 \) (same size)
• Option d: \( \frac{4}{3} \) (greater than 1, image larger)

Answer:

d. \( \frac{4}{3} \)