Question

what a hot streak, a 4 ... scale factor is \\(\frac{3}{2}\\)
which figure correctly shows \\(\triangle abc\\) using the solid line?
choose 1 answer:
a
figure a
b
figure b
c
figure c

Explanation:

Step1: Analyze Scale Factor

The scale factor is $\frac{3}{2}$, which is greater than 1, so the image $\triangle A'B'C'$ should be an enlargement of $\triangle ABC$.

Step2: Compare Figures

• Option A: The triangle $\triangle A'B'C'$ is larger than $\triangle ABC$ (since scale factor > 1) and maintains the same shape and relative position with respect to the center of dilation \( P \).
• Option B: The triangle is smaller, which would correspond to a scale factor less than 1, so it's incorrect.
• Option C: The shape and orientation don't match the expected enlargement from the scale factor $\frac{3}{2}$ and the center of dilation \( P \).

Answer:

A. The figure in option A (with \( A' \), \( B' \), \( C' \) forming a larger triangle around \( \triangle ABC \) relative to \( P \))