Question

line segment st is dilated to create line segment st using the dilation rule ( d_{q,2.25} ). what is x, the distance between points s and s? ( x = 2.25 ) units ( x = 2.5 ) units ( x = 4.25 ) units ( x = 4.5 ) units

Explanation:

Step1: Recall the dilation formula

For a dilation with center \(Q\) and scale factor \(k\), if a point \(A\) is dilated to \(A'\), then \(QA'=k\times QA\). Here, the scale factor \(k = 2.25\), and we know that \(QS'=QS + x\). Also, from the property of dilation \(\frac{QT'}{QT}=k\) (we can use the ratio of segments from the center of dilation). And \(QS'=k\times QS\).

Step2: Substitute the values

We know \(QS'=QS + x\), and \(k = 2.25\), \(QS = 2\). So \(QS'=2.25\times2\). Since \(QS'=2 + x\), then \(2 + x=2.25\times2\).

Step3: Solve for \(x\)

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Answer:

\(x = 2.5\) units.