Question

You are graphing Rectangle ABCD in the coordinate plane. The following are three of the vertices of therectangle: A(-5,–8), B(-5,0), and C(-2,0).what are the coordinates of point D?

Answer 1

Here, we want to get the coordinates of point D

Mathematically, for a rectangle, the diagonals will intersect and that means that the midpoint of the diagonals of the rectangle will be equal

So we have the diagonals intersect

We have the diagonals AC and BD

Let us start with the coordinates of the midpoint of AC

We can find this by the use of the midpoint formula

We have this as;

`\begin{gathered} (x,y)\text{ = (}(x_1+x_2)/(2),\text{ }(y_1+y_2)/(2)) \\ \\ (x,y)\text{ = (}(-5-2)/(2),(-8-0)/(2))=\text{ (-3.5,-4)} \end{gathered}`

So, the second diagonal will have this same exact midpoint

For the diagonal BD, we have;