Question

△abc is the image of △abc under a dilation whose center is a and scale factor is 3/4. which figure correctly shows △abc using the solid line? choose 1 answer:

Explanation:

Step1: Understand the dilation

Dilation is a transformation that changes the size of a figure. The center of dilation is \(A\), and the scale factor is \(\frac{3}{4}\). This means that all points of \(\triangle ABC\) (except \(A\)) are moved towards \(A\) such that the distance from \(A\) to each new point (\(A'\), \(B'\), \(C'\)) is \(\frac{3}{4}\) of the original distance from \(A\) to \(B\) and \(A\) to \(C\). Since \(A\) is the center of dilation, \(A = A'\).

Step2: Analyze Option A

In Option A, \(A'=A\) (correct as center of dilation), and \(B'\) and \(C'\) are located such that \(AB'=\frac{3}{4}AB\) and \(AC'=\frac{3}{4}AC\) (by visual inspection of the relative positions with respect to center \(A\)).

Step3: Analyze Option B

In Option B, \(A'
eq A\). But since the center of dilation is \(A\), \(A\) should remain the same in the image \(\triangle A'B'C'\). So Option B is incorrect.

Answer:

A.