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 from each point to the line \(y = - 1\)

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

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 \(y_{reflected}=-1-(y + 1)\) (if \(y<-1\)) or \(y_{reflected}=-1+( - 1 - y)\) (general formula). Simplifying, \(y_{reflected}=-2 - y\). The \(x\) - coordinate remains the same, i.e., \(x_{reflected}=x\)

Suppose the original points of the figure are \((2,-5)\), \((4,-4)\), \((8,-8)\)

• For the point \((2,-5)\):

\(y_{reflected}=-2-(-5)=3\), so the reflected point is \((2,3)\)

• For the point \((4,-4)\):

\(y_{reflected}=-2-(-4) = 2\), so the reflected point is \((4,2)\)

• For the point \((8,-8)\):

\(y_{reflected}=-2-(-8)=6\), so the reflected point is \((8,6)\)

Answer:

Plot the points \((2,3)\), \((4,2)\) and \((8,6)\)