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 \(k\), if a point \(P\) is dilated to \(P'\), then \(QP'=k\times QP\). Here, the scale factor \(k = 0.15\). Let \(QA=x + 2.4\) and \(QA'=2.4\). Since \(QA'=k\times QA\), we have \(2.4=0.15\times(x + 2.4)\).

Step2: Solve the equation for \(x\)

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 \(\frac{2.4}{0.15}=\frac{240}{15}=16\), the equation becomes \(16=x + 2.4\).
Then, subtract \(2.4\) from both sides: \(x=16 - 2.4\).

Step3: Calculate the value of \(x\)

\(x = 13.6\)

Answer:

13.6 units