Question

if p = (-2,3), find: r_{x = 2}(p)

Explanation:

Step1: Calculate the distance from the point to the line \(x = 2\)

The distance between \(x=-2\) and \(x = 2\) is \(d=\vert-2 - 2\vert=\vert-4\vert = 4\).

Step2: Find the \(x\) - coordinate of the reflected point

Since we are reflecting over the line \(x = 2\), the \(x\) - coordinate of the reflected point \(P'\) is \(2+4=6\).

Step3: Determine the \(y\) - coordinate of the reflected point

When reflecting a point \((x,y)\) over a vertical line \(x = a\), the \(y\) - coordinate remains the same. So the \(y\) - coordinate of the reflected point is \(y = 3\).

Answer:

\((6,3)\)