Question

1. explain why this dilation is incorrect

Explanation:

Step1: Recall Dilation Definition

Dilation requires a scale factor and a center, with all corresponding points' distances from the center in proportion (scale factor).

Step2: Analyze the Diagram

In the given dilation attempt, the lines from the center to corresponding vertices should have consistent scale factor. But here, the ratios of distances from the center to the original and image vertices are not equal (e.g., one side's ratio ≠ another's), violating dilation's proportionality.

Step3: Conclude the Error

Since dilation needs all corresponding segments from the center to be scaled by the same factor, and this diagram fails that (unequal scale factors for different sides), the dilation is incorrect.

Answer:

The dilation is incorrect because in a dilation, the distance from the center of dilation to each corresponding vertex of the original and image figures must be in the same ratio (scale factor). In this diagram, the ratios of the distances from the center to the vertices of the original triangle and the image triangle are not equal for all corresponding vertices, violating the definition of dilation.