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:

planation:

Step1: Recall the dilation formula

The dilation formula is \(QA'=0.15\times QA\). Let \(QA = x + 2.4\). Then \(QA'=2.4\).

Step2: Substitute into the formula

Substitute into \(QA'=0.15\times QA\), we get \(2.4 = 0.15\times(x + 2.4)\).

Step3: Solve the equation

First, divide both sides of the equation \(2.4 = 0.15\times(x + 2.4)\) by \(0.15\): \(\frac{2.4}{0.15}=x + 2.4\). Since \(\frac{2.4}{0.15}=16\), then \(16=x + 2.4\). Subtract \(2.4\) from both sides: \(x=16 - 2.4\).

Answer:

\(13.6\) units