Question

which graph shows a dilation?

Explanation:

Step1: Recall Dilation Definition

Dilation is a transformation that changes the size of a figure but not its shape. The center of dilation is a fixed point, and corresponding points are scaled by a scale factor relative to this center.

Step2: Analyze Each Graph

• First Graph: Check if the larger figure is a scaled version (same shape, different size) of the smaller one, centered at the same point.
• Second Graph: The smaller figure seems distorted in shape (not a uniform scale), so not dilation.
• Third Graph: The larger figure appears to be a scaled (enlarged) version of the smaller one, with the same shape and centered at the same point (the origin or the center of the smaller figure).
• Fourth Graph: The smaller figure's position or shape relation doesn't show uniform scaling.

Answer:

The Third Graph (the one from the left, third in sequence)