Question

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? options: a. \\( \frac{3}{5} \\) b. \\( \frac{11}{17} \\) c. 1 d. 1.5

Explanation:

Step1: Recall Dilation Scale Factor

A dilation with a scale factor \( k \) transforms a figure. If \( k > 1 \), the image is larger than the original; if \( 0 < k < 1 \), the image is smaller. We need to find which option has \( k > 1 \).

Step2: Analyze Each Option

• Option A: \( \frac{3}{4}=0.75 \), \( 0.75 < 1 \) (smaller).
• Option B: \( \frac{11}{12}\approx0.92 \), \( 0.92 < 1 \) (smaller).
• Option C: \( 1 \), scale factor 1 means image is same size.
• Option D: \( 2.5 \), \( 2.5 > 1 \) (larger).

Answer:

D. 2.5