Question

reflect the figure over the line $y=-1$.
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 \(y = - 1\)

Let's assume a point \((x,y)\) in the original figure. The distance between the point \((x,y)\) and the line \(y=-1\) is \(d=y - (-1)=y + 1\)

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

For a reflection over the line \(y=-1\), the formula for the \(y\) - coordinate of the reflected point \((x,y')\) is \(y'=-1-(y + 1)=-y - 2\). The \(x\) - coordinate of the point remains the same during a horizontal reflection (reflection over a horizontal line \(y = k\)).

For example, if we have a point \((2,-3)\):
The distance from \(y=-3\) to \(y = - 1\) is \(d=-1-(-3)=2\). The reflected \(y\) - coordinate is \(y'=-1 + 2=1\), so the reflected point is \((2,1)\)

If we have a point \((8,-7)\):
The distance from \(y = - 7\) to \(y=-1\) is \(d=-1-(-7)=6\). The reflected \(y\) - coordinate is \(y'=-1+6 = 5\), so the reflected point is \((8,5)\)

If we have a point \((2,-9)\):
The distance from \(y=-9\) to \(y=-1\) is \(d=-1-(-9)=8\). The reflected \(y\) - coordinate is \(y'=-1 + 8=7\), so the reflected point is \((2,7)\)

Answer:

Plot the points \((2,1)\), \((8,5)\) and \((2,7)\)