Question

1. triangle abc is dilated to produce △abc with scale factor $\frac{3}{4}$. which statement describes the relationship between the two triangles? a. △abc is an enlargement of △abc. b. △abc is a reduction of △abc. c. △abc ≅ △abc d. △abc is a mirror image of △abc.

Explanation:

Step1: Recall dilation rule

If the scale - factor $k$ of a dilation satisfies $0

Step2: Analyze each option

• Option a: An enlargement occurs when $k>1$, so this is incorrect.
• Option b: Since $0 <\frac{3}{4}<1$, $\triangle A'B'C'$ is a reduction of $\triangle ABC$, this is correct.
• Option c: $\triangle A'B'C'\cong\triangle ABC$ occurs when $k = 1$, so this is incorrect.
• Option d: A dilation is not a reflection (mirror image), so this is incorrect.

Answer:

B. $\triangle A'B'C'$ is a reduction of $\triangle ABC$