Question

reflect the figure over the line y = 3. plot all of the points of the reflected figure. you may click a plotted point to delete it.

Explanation:

Step1: Identify original points

First, find the coordinates of the original triangle's vertices. From the graph:

• Point 1: \((1, 6)\)
• Point 2: \((3, 9)\)
• Point 3: \((6, 7)\)

Step2: Reflect over \(y = 3\)

The formula for reflecting a point \((x, y)\) over the horizontal line \(y = k\) is \((x, 2k - y)\). Here, \(k = 3\), so the reflection formula is \((x, 2(3)-y)=(x, 6 - y)\).

For \((1, 6)\):

\(y\)-coordinate: \(6 - 6 = 0\), so reflected point is \((1, 0)\).

For \((3, 9)\):

\(y\)-coordinate: \(6 - 9 = -3\), so reflected point is \((3, -3)\).

For \((6, 7)\):

\(y\)-coordinate: \(6 - 7 = -1\), so reflected point is \((6, -1)\).

Answer:

The reflected points are \((1, 0)\), \((3, -3)\), and \((6, -1)\). To plot them, mark these coordinates on the graph.