Question

which image shows triangle abc dilated by a scale factor of 3 centered at the point b?

Explanation:

Step1: Understand dilation at a center

When dilating a figure centered at a point (here \(B\)), the center point \(B\) remains unchanged.

Step2: Check scale - factor effect

A scale factor of \(3\) means the distance from \(B\) to other points (like \(A\) and \(C\)) in the original triangle is tripled.
For example, if we consider the vector from \(B\) to \(A\) (or \(B\) to \(C\)) in \(\triangle ABC\), in the dilated triangle \(\triangle A'B'C'\), the vectors from \(B\) to \(A'\) and \(B\) to \(C'\) should be three - times the length of vectors from \(B\) to \(A\) and \(B\) to \(C\) respectively.

Looking at the top - right graph:

• Point \(B\) is fixed (as it is the center of dilation).
• The length of \(BA'\) is \(3\) times the length of \(BA\) and the length of \(BC'\) is \(3\) times the length of \(BC\)

Answer:

The top - right graph.