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 points of the triangle. From the graph, the vertices seem to be:

• Point 1: \((1, 3)\)
• Point 2: \((7, 7)\)
• Point 3: \((8, 0)\)

To reflect a point \((x, y)\) over the line \(y = k\), the formula for the new \(y\)-coordinate is \(y' = 2k - y\). Here, \(k = -1\), so \(y' = 2(-1) - y = -2 - y\). The \(x\)-coordinate remains the same.

Step 1: Reflect Point \((1, 3)\)

For \(x = 1\), \(y = 3\):
\(y' = -2 - 3 = -5\)
So the reflected point is \((1, -5)\)

Step 2: Reflect Point \((7, 7)\)

For \(x = 7\), \(y = 7\):
\(y' = -2 - 7 = -9\)
So the reflected point is \((7, -9)\)

Step 3: Reflect Point \((8, 0)\)

For \(x = 8\), \(y = 0\):
\(y' = -2 - 0 = -2\)
So the reflected point is \((8, -2)\)

Answer:

The reflected points are \((1, -5)\), \((7, -9)\), and \((8, -2)\). You can plot these points on the graph.