Question

question
reflect the figure over the line ( y = -2 ).
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 \(y = - 2\)

Let's assume a point \((x,y)\). The distance \(d\) from the point \((x,y)\) to the line \(y=-2\) is \(d=\vert y - (-2)\vert=\vert y + 2\vert\).

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

For a reflection over the line \(y = - 2\), if the original point has coordinates \((x,y)\), the formula for the \(y\) - coordinate of the reflected point \((x,y')\) is \(y'=-2-(y + 2)\). Simplifying, we get \(y'=-4 - y\). The \(x\) - coordinate remains the same, i.e., \(x'=x\).

Suppose the original triangle has vertices \(A(x_1,y_1)\), \(B(x_2,y_2)\), \(C(x_3,y_3)\). The reflected vertices will be \(A'(x_1,-4 - y_1)\), \(B'(x_2,-4 - y_2)\), \(C'(x_3,-4 - y_3)\)

Answer:

Plot the new triangle with vertices obtained by using the rule \((x,y)\to(x,-4 - y)\) for each vertex of the original triangle.