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: Use dilation formula

The dilation rule \(D_{Q,0.15}\) means the scale factor \(k = 0.15\). Let the distance from \(Q\) to \(A\) be \(QA\) and from \(Q\) to \(A'\) be \(QA'\). We know that \(QA'=0.15\times QA\). Also, \(QA=QA'+x\). Since \(QA' = 2.4\), then \(2.4=0.15\times QA\).

Step2: Solve for \(QA\)

From \(2.4 = 0.15\times QA\), we can find \(QA=\frac{2.4}{0.15}=16\).

Step3: Calculate \(x\)

Since \(QA=QA'+x\), then \(x=QA - QA'\). Substitute \(QA = 16\) and \(QA'=2.4\) into the formula, we get \(x=16 - 2.4=13.6\).

Answer:

13.6 units