Question

reflect the figure over the line x = 4. 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 \(x = 4\), we use the formula for reflection over a vertical line \(x = a\): the new \(x\)-coordinate is \(2a - x\), and the \(y\)-coordinate remains the same. Here, \(a = 4\), so the formula becomes \(x' = 2(4)-x=8 - x\) and \(y' = y\).

First, we identify the original points of the figure. Let's assume the original points (from the graph) are:

• Point 1: \((5, 5)\)
• Point 2: \((6, 7)\)
• Point 3: \((8, 8)\)
• Point 4: \((9, 4)\)

Step 1: Reflect \((5, 5)\)

Using the formula \(x' = 8 - 5 = 3\), \(y' = 5\). So the reflected point is \((3, 5)\).

Step 2: Reflect \((6, 7)\)

\(x' = 8 - 6 = 2\), \(y' = 7\). Reflected point: \((2, 7)\).

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

\(x' = 8 - 8 = 0\), \(y' = 8\). Reflected point: \((0, 8)\).

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

\(x' = 8 - 9 = -1\), \(y' = 4\). Reflected point: \((-1, 4)\).

Now, we plot these reflected points \((3, 5)\), \((2, 7)\), \((0, 8)\), and \((-1, 4)\) on the coordinate plane.

Answer:

The reflected points are \((3, 5)\), \((2, 7)\), \((0, 8)\), and \((-1, 4)\) (plot these points on the given coordinate system).