Question

7 ( x = 2 ) is dilated by a scale factor of ( \frac{1}{2} ) with the center as ( (10,-5) ). graph the dilated line.

Explanation:

Step1: Find the distance between the line \(x = 2\) and the center of dilation \((10,-5)\)

The distance \(d\) between \(x = 2\) and \(x=10\) (since the center has \(x -\) coordinate \(10\)) is \(|10 - 2|=8\)

Step2: Apply the scale factor

After dilation with scale factor \(k=\frac{1}{2}\), the new distance \(d_{new}=k\times d=\frac{1}{2}\times8 = 4\)

Step3: Determine the equation of the dilated line

Since the original line \(x = 2\) is to the left of the center \(x = 10\), the dilated line will be to the left of \(x = 10\). Let the \(x -\) coordinate of the dilated line be \(x\). Then \(|10 - x|=4\) and \(x=10 - 4=6\)

Answer:

The equation of the dilated line is \(x = 6\)