Question

reflect the figure over the line y = -1. plot all of the points of the reflected figure. you may click a plotted point to delete it.

Explanation:

First, identify the original vertices of the triangle. From the graph, the original points seem to be \((2, 6)\), \((8, 6)\), and \((7, 2)\).

Step1: Reflect \((2, 6)\) over \(y = -1\)

The formula for reflecting a point \((x, y)\) over the line \(y = k\) is \((x, 2k - y)\). Here, \(k = -1\), so for \((2, 6)\):
\(2k - y = 2(-1) - 6 = -2 - 6 = -8\). So the reflected point is \((2, -8)\).

Step2: Reflect \((8, 6)\) over \(y = -1\)

Using the same formula, \(2k - y = 2(-1) - 6 = -8\). So the reflected point is \((8, -8)\).

Step3: Reflect \((7, 2)\) over \(y = -1\)

\(2k - y = 2(-1) - 2 = -2 - 2 = -4\). So the reflected point is \((7, -4)\).

Answer:

The reflected points are \((2, -8)\), \((8, -8)\), and \((7, -4)\). Plot these points on the graph.