Question

practice solving dilation problems. 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 is given by \(k=\frac{\text{length of image segment}}{\text{length of original segment}}\).

Step2: Identify the lengths

For the dilation of segment \(SU\) to \(S'U'\) with center \(Q\), we can use the segments from the center of dilation. Let's take \(QS'\) and \(QS\). \(QS' = QS + S'S\), but from the figure, if we consider the general formula using the ratio of \(QS'\) to \(QS\) (or \(QU'\) to \(QU\)). Here, \(QS'=4 + 4=8\) and \(QS = 4\), or using \(QU'=5 + 5 = 10\) and \(QU=5\). Using \(k=\frac{QS'}{QS}\), we have \(k=\frac{8}{4}\). Using \(k = \frac{QU'}{QU}\), we have \(k=\frac{10}{5}\).

Answer:

\(2\)