Question

the vertices of triangle abc are a(-3,4), b(-2,5), and c(-4,2). if triangle abc is reflected across the line y=-2, find the coordinates of the vertex b. the coordinates of b after a reflection across y=-2 are (type your answer as an ordered pair in parentheses).

Explanation:

Step1: Calculate the distance between y - coordinate of B and the line y = - 2

The y - coordinate of point B is \(y = 5\). The line of reflection is \(y=-2\). The distance \(d\) between \(y = 5\) and \(y=-2\) is \(d=\vert5-(-2)\vert=\vert5 + 2\vert=7\).

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

Since we are reflecting across the line \(y=-2\), the new y - coordinate \(y'\) of the reflected point \(B'\) is \(y'=-2-7=-9\). The x - coordinate of a point reflected across a horizontal line \(y = k\) remains the same. The x - coordinate of point B is \(x=-2\).

Answer:

\((-2,-9)\)