Question

line segment ab was dilated to create line segment ab using the dilation rule ( d_{q,0.15} ). what is x, the distance between points a and a? 2.4 units 4.8 units 13.6 units 14.4 units

Explanation:

Step1: Recall the dilation formula

For a dilation with center \(Q\) and scale factor \(k = 0.15\), if \(QA'=2.4\) and \(QA=QA'+x\), and the formula for dilation is \(QA'=k\times QA\). Let \(QA = y\), then \(y=\frac{QA'}{k}\).

Step2: Calculate \(QA\)

Since \(k = 0.15\) and \(QA'=2.4\), using \(y=\frac{QA'}{k}\), we have \(y=\frac{2.4}{0.15}=16\).

Step3: Calculate \(x\)

We know that \(QA=QA'+x\), so \(x = QA - QA'\). Substituting \(QA = 16\) and \(QA'=2.4\), we get \(x=16 - 2.4=13.6\).

Answer:

13.6 units