Question

line segment ab is dilated to create line segment ab using point q as the center of dilation. what is the scale factor? 1, 1.25, 2, 2.5

Explanation:

Step1: Recall Dilation Scale Factor

The scale factor of a dilation is the ratio of the distance from the center of dilation to a point on the image (\(QA'\)) to the distance from the center of dilation to the corresponding point on the original figure (\(QA\)).

Step2: Calculate Distances

From the diagram, \(QA = 1.25\) and \(QA'=QA + AA'= 1.25+1.25 = 2.5\).

Step3: Compute Scale Factor

The scale factor \(k=\frac{QA'}{QA}=\frac{2.5}{1.25} = 2\).

Answer:

2