Question

unit 1, lesson 1: what are scaled copies? are any of the figures b, c, or d scaled copies of figure a? explain how you know.

Explanation:

Step1: Analyze figure B

Check if all sides of B are in proportion to A. The vertical side of A is \( 4 \) units, and of B is \( 6 \) units (\( \frac{6}{4}=1.5 \)). The horizontal side of A is \( 2 \) units, and of B is \( 3 \) units (\( \frac{3}{2} = 1.5 \)). All corresponding sides have the same scale factor.

Step2: Analyze figure C

The vertical side of A is \( 4 \) units, and of C is \( 6 \) units (\( \frac{6}{4}=1.5 \)). But the horizontal side of A is \( 2 \) units, and of C is \( 2 \) units (\( \frac{2}{2}=1 \)). The scale factors are not the same.

Step3: Analyze figure D

The vertical side of A is \( 4 \) units, and of D is \( 6 \) units (\( \frac{6}{4}=1.5 \)). The horizontal side of A is \( 2 \) units, and of D is \( 4 \) units (\( \frac{4}{2}=2 \)). The scale factors are not the same.

Answer:

Figure B is a scaled - copy of figure A. Figures C and D are not. Because for figure B, all corresponding side lengths have the same scale factor (\( 1.5 \)), while for figures C and D, the scale factors of corresponding side lengths are not equal.