Question

line segment su is dilated to create su using point q as the center of dilation. the scale factor of the dilation is

Explanation:

Step1: Recall the formula for scale factor

The scale factor \(k\) of a dilation with center \(Q\) is given by \(k=\frac{QS'}{QS}\) (or \(\frac{QU'}{QU}\))

Step2: Substitute the values

From the figure, \(QS' = 4\) and \(QS=4\). So, \(k=\frac{QS'}{QS}=\frac{4 + 4}{4}\) (since \(QS'=QQ + S'Q\) and \(QS = QS\) in terms of segments from center \(Q\)). Wait, no, actually, if we consider the general formula for dilation: if a point \(P\) is dilated to \(P'\) with center \(O\), the scale factor \(k=\frac{OP'}{OP}\). Here, for point \(S\) dilated to \(S'\) with center \(Q\), \(QS'=4 + 4=8\) (assuming the length from \(Q\) to \(S'\) is composed of two segments of length \(4\)) and \(QS = 4\). So \(k=\frac{QS'}{QS}=\frac{8}{4}=2\)

Answer:

\(2\)