Question

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

Explanation:

Step1: Recall the formula for scale factor

The scale factor \(k\) for a dilation with center \(Q\) is given by \(k=\frac{QA'}{QA}\) (or \(\frac{QB'}{QB}\) since the scale factor is the same for all corresponding points in a dilation).

Step2: Substitute the values

From the diagram, \(QA' = QA + 1.25\) (wait, no, actually, if \(QA = 1.25\) and \(QA'=1.25 + 1.25=2.5\) (no, wrong approach). Wait, actually, the scale factor \(k=\frac{\text{length of image segment}}{\text{length of pre - image segment}}\). But also, using the distance from the center of dilation: \(k=\frac{QA'}{QA}\). If \(QA'=(QA + 1.25)\) no, wait looking at the segments from \(Q\) to \(A\) is \(1.25\) units and from \(Q\) to \(A'\) is \(1.25+1.25 = 2.5\) units. So \(k=\frac{QA'}{QA}=\frac{2.5}{1.25}=2\)

Answer:

\(2\)