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:

First, we identify the coordinates of the original triangle's vertices. From the graph, the vertices are:

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

To reflect a point \((x, y)\) over the line \(y = k\), the formula for the reflected point \((x', y')\) is \(x' = x\) and \(y' = 2k - y\). Here, \(k = 3\), so the formula becomes \(y' = 2(3) - y = 6 - y\).

Step 1: Reflect Point 1 \((1, 6)\)

Using the formula \(y' = 6 - y\), substitute \(y = 6\):
\(y' = 6 - 6 = 0\)
So the reflected point is \((1, 0)\).

Step 2: Reflect Point 2 \((3, 9)\)

Substitute \(y = 9\) into \(y' = 6 - y\):
\(y' = 6 - 9 = -3\)
So the reflected point is \((3, -3)\).

Step 3: Reflect Point 3 \((6, 7)\)

Substitute \(y = 7\) into \(y' = 6 - y\):
\(y' = 6 - 7 = -1\)
So the reflected point is \((6, -1)\).

Answer:

The reflected points are \((1, 0)\), \((3, -3)\), and \((6, -1)\). To plot the reflected figure, mark these three points on the coordinate plane.