Question

nc.7.g.1 2. priya drew a triangle with side lengths 3, 4, 5. she wants to draw a smaller scaled copy. which of the following are scale - factors she could use to scale the triangle smaller? select all that apply. a. 1 b. 3.5 c. 0.5 d. 1/3 e. - 4 f. - 4/7

Explanation:

Step1: Recall scale - factor concept

A scale factor \(k\) is used to create a scaled - copy of a figure. If \(|k|> 1\), the new figure is larger; if \(|k| = 1\), the new figure is the same size; if \(|k|<1\), the new figure is smaller.

Step2: Analyze each option

• Option A: If \(k = 1\), the scaled - copy is the same size as the original.
• Option B: If \(k=3.5>1\), the scaled - copy is larger.
• Option C: If \(k = 0.5<1\), the scaled - copy is smaller.
• Option D: If \(k=\frac{1}{3}<1\), the scaled - copy is smaller.
• Option E: A negative scale factor changes the orientation, but \(| - 4|=4>1\), so the scaled - copy is larger.
• Option F: If \(k =-\frac{4}{7}\), \(|-\frac{4}{7}|=\frac{4}{7}<1\), the scaled - copy is smaller.

Answer:

C. 0.5, D. \(\frac{1}{3}\), F. \(-\frac{4}{7}\)