Question

if ( p = (-2, 4) ), then find: ( r_{y = 1}(p) ) ( (square, square) )

Explanation:

Step1: Find the distance between the y - coordinate of point P and the line \(y = 1\)

The y - coordinate of point \(P(-2,4)\) is \(y_{P}=4\). The line is \(y = 1\). The distance \(d\) is \(d=\vert4 - 1\vert=3\).

Step2: Calculate the new y - coordinate after reflection over \(y = 1\)

When reflecting a point \((x,y)\) over the line \(y = k\), the formula for the new y - coordinate \(y'\) is \(y'=2k - y\). Here \(k = 1\) and \(y = 4\), so \(y'=2\times1-4=-2\). The x - coordinate remains the same since reflection over a horizontal line \(y = k\) does not change the x - value.

Answer:

\((-2,-2)\)