Question

suppose line h is the line with equation y = - 1. given a(8, - 5), b(6,4), and c( - 1, - 7), what are the coordinates of the vertices of \\( \triangle a ^ { \prime } b ^ { \prime } c ^ { \prime } \\) for the reflection? \\( r _ { h } \\) a (type an ordered pair.)

Explanation:

Step1: Calculate the distance from the y - coordinate of point A to the line \(y = - 1\)

The formula for the distance \(d\) between a point \((x,y)\) and the line \(y = k\) is \(d=\vert y - k\vert\). For point \(A(8,-5)\) and \(k=-1\), \(d=\vert-5-(-1)\vert=\vert-5 + 1\vert=\vert-4\vert = 4\)

Step2: Find the y - coordinate of \(A'\)

Since the reflection over the line \(y=-1\), the y - coordinate of \(A'\) is \(y=-1+4 = 3\) (the x - coordinate remains the same). So \(A'=(8,3)\)

Answer:

\((8,3)\)