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:

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

First, identify the original points from the graph:

• Let's assume the original points are \((1, 6)\), \((2, 4)\), \((8, 4)\), \((9, 9)\) (by looking at the plotted points).

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

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

Step 2: Reflect \((2, 4)\)

Substitute \(y = 4\) into \(y' = 6 - y\):
\(y'=6 - 4 = 2\). So the reflected point is \((2, 2)\).

Step 3: Reflect \((8, 4)\)

Substitute \(y = 4\) into \(y' = 6 - y\):
\(y'=6 - 4=2\). So the reflected point is \((8, 2)\).

Step 4: Reflect \((9, 9)\)

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

Answer:

The reflected points are \((1, 0)\), \((2, 2)\), \((8, 2)\), \((9, - 3)\). To plot them, mark these coordinates on the coordinate plane.