Question

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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 the y - coordinate of point B and the line y = - 2

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

Step2: Find the y - coordinate of the reflected point B'

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

Answer:

\((-2,-9)\)