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: Find the distance between each point and the line \(y = 3\)

Let's assume the original points are \((x_1,y_1)\), \((x_2,y_2)\), \((x_3,y_3)\). The distance \(d\) between a point \((x,y)\) and the line \(y = 3\) is \(d=\vert y - 3\vert\).

Step2: Calculate the \(y\) - coordinate of the reflected points

For a point \((x,y)\) reflected over the line \(y = 3\), the formula for the \(y\) - coordinate of the reflected point \((x,y')\) is \(y'=3+(3 - y)=6 - y\). The \(x\) - coordinate remains the same.

Suppose the original points are \((1,5)\), \((3,5)\), \((6,4)\), \((7,9)\)

• For the point \((1,5)\): \(y'=6 - 5=1\), so the reflected point is \((1,1)\)
• For the point \((3,5)\): \(y'=6 - 5 = 1\), so the reflected point is \((3,1)\)
• For the point \((6,4)\): \(y'=6 - 4=2\), so the reflected point is \((6,2)\)
• For the point \((7,9)\): \(y'=6 - 9=- 3\), so the reflected point is \((7,-3)\)

Answer:

Plot the points \((1,1)\), \((3,1)\), \((6,2)\), \((7,-3)\) (assuming the original non - labeled points in the figure have \(x\) and \(y\) coordinates as in the example above. If you can provide the exact original points, a more precise answer can be given)