Question

this question has two parts.
isosceles triangle efg is dilated to create triangle efg, as shown.

part a
complete the sentence to describe the scale factor of the dilation.
since the size of triangle efg is blank triangle efg, the scale factor of the dilation is blank.

part b
what is the scale factor of the dilation?
number pad with digits 0-9

(note: the image also shows a paper with conversion formulas and the slope formula, but the main problem is about the dilated triangle.)

Explanation:

Step1: Analyze the dilation

Dilation scale factor is the ratio of corresponding sides of the image to the original. Here, triangle \( E'F'G' \) is the image of \( EFG \) after dilation. We can take corresponding sides, e.g., \( F'G' = 9 \) and \( FG = 12 \), or \( E'G' = 11.25 \) and \( EG = 15 \).

Step2: Calculate the scale factor

Using \( F'G' \) and \( FG \): scale factor \( = \frac{F'G'}{FG} = \frac{9}{12} = \frac{3}{4} = 0.75 \). Or using \( E'G' \) and \( EG \): \( \frac{11.25}{15} = 0.75 \). Also, since \( E'F'G' \) is smaller than \( EFG \), \( EFG \) is larger than \( E'F'G' \), so scale factor is less than 1.

Answer:

Part A:

Since the size of triangle \( EFG \) is larger than triangle \( E'F'G' \), the scale factor of the dilation is \( 0.75 \) (or \( \frac{3}{4} \)).

Part B:

The scale factor of the dilation is \( \boldsymbol{0.75} \) (or \( \boldsymbol{\frac{3}{4}} \)).