Question

drag the blue points to create the reflection of the polygon over the line x = 7.
show your work here

Explanation:

Step1: Recall Reflection Over Vertical Line

For a point \((x,y)\) reflected over the vertical line \(x = a\), the formula for the reflected point \((x',y')\) is \(x'=2a - x\) and \(y' = y\). Here, \(a = 7\).

Step2: Identify Original Points

Let's identify the original blue points. From the graph:

• First point: \((0,6)\) (on the y - axis, \(x = 0\), \(y = 6\))
• Second point: \((9,6)\) (since it's on \(y = 6\), \(x = 9\))
• Third point: \((5,-6)\) ( \(x = 5\), \(y=-6\))

Step3: Reflect Each Point

For \((0,6)\):

Using the formula \(x'=2\times7 - 0=14\), \(y' = 6\). So the reflected point is \((14,6)\).

For \((9,6)\):

\(x'=2\times7 - 9 = 14 - 9 = 5\), \(y' = 6\). So the reflected point is \((5,6)\).

For \((5,-6)\):

\(x'=2\times7 - 5=14 - 5 = 9\), \(y'=-6\). So the reflected point is \((9,-6)\).

Step4: Plot Reflected Points

Plot the points \((14,6)\), \((5,6)\), and \((9,-6)\) and connect them to form the reflected polygon.

Answer:

To reflect the polygon over \(x = 7\), use the reflection formula \(x'=14 - x\) (since \(2\times7=14\)) for each point \((x,y)\) (keeping \(y\) the same). Reflect \((0,6)\) to \((14,6)\), \((9,6)\) to \((5,6)\), and \((5,-6)\) to \((9,-6)\), then connect these reflected points.