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: a b

Explanation:

Step1: Recall the property of dilation

Dilation is a transformation that changes the size of a figure but not its shape. When the center of dilation is a vertex (in this case \(A\)), that vertex remains the same in the dilated figure. Since the scale factor is \(\frac{3}{4}< 1\), the dilated triangle \(\triangle A'B'C'\) will be smaller than \(\triangle ABC\) and \(A = A'\).

Step2: Analyze Option A and Option B

• In Option A, \(A'\) is a new point inside \(\triangle ABC\). But when the center of dilation is \(A\), \(A\) should coincide with \(A'\) in the dilated figure.
• In Option B, \(A = A'\) (because the center of dilation is \(A\)), and the other points \(B'\) and \(C'\) are located such that \(AB'=\frac{3}{4}AB\) and \(AC'=\frac{3}{4}AC\) (since the scale factor is \(\frac{3}{4}\)), which is consistent with the definition of dilation with center \(A\) and scale factor \(\frac{3}{4}\).

Answer:

B.