Question

the vertices of \\( \triangle a b c \\) are \\( a(-3,5), b(-2,3) \\), and \\( c(-5,2) \\). if \\( \triangle a b c \\) is reflected across the line \\( y=-2 \\) to produce the image \\( \triangle a b^{prime} c \\), find the coordinates of the vertex \\( b^{prime} \\).

the coordinates of \\( b^{prime} \\) after a reflection across the line \\( y=-2 \\) are
(type an ordered pair.)

Explanation:

Step1: Calculate the distance between the y - coordinate of point B and the line \(y = - 2\)

The y - coordinate of point \(B(-2,3)\) is \(y = 3\). The distance \(d\) between \(y = 3\) and \(y=-2\) is \(d=\vert3-(-2)\vert=\vert3 + 2\vert=5\)

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

Since we are reflecting across the line \(y=-2\), the new y - coordinate \(y'\) of \(B'\) is \(y'=-2-5=-7\) (because the reflection is in the direction away from the original y - coordinate). The x - coordinate remains the same during a reflection across a horizontal line. The x - coordinate of point \(B\) is \(x=-2\)

Answer:

\((-2,-7)\)