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: Understand the dilation rule

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

Step2: Find \(QA\)

Since \(k = 0.15\) and \(QA' = 2.4\), from \(QA'=k\times QA\), we can solve for \(QA\) as \(QA=\frac{QA'}{k}\). Substituting the values, \(QA=\frac{2.4}{0.15}=16\).

Step3: Calculate \(x\)

The distance \(x = QA - QA'\). Substituting \(QA = 16\) and \(QA'=2.4\), we get \(x=16 - 2.4=13.6\).

Answer:

13.6 units