Question

1. triangle ( a b c ) is taken to triangle ( a ^ { prime } b ^ { prime } c ^ { prime } ) by a dilation. which of these scale factors for the dilation would result in an image that was larger than the original figure?

a. ( \frac { 3 } { 5 } )
b. ( \frac { 13 } { 17 } )
c. 1
d. ( \frac { 4 } { 3 } )

Explanation:

Step1: Recall the rule of dilation

When the scale factor \(k> 1\), the image is larger than the original figure. When \(0 < k<1\), the image is smaller than the original figure. When \(k = 1\), the image is congruent to the original figure.

Step2: Analyze each option

• Option A: \(\frac{3}{5}=0.6<1\), so the image is smaller than the original.
• Option B: \(\frac{13}{17}\approx0.765<1\), so the image is smaller than the original.
• Option C: \(k = 1\), the image is congruent to the original.
• Option D: \(\frac{4}{3}\approx1.33>1\), so the image is larger than the original.

Answer:

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