Question

Parallelogram ABCD has vertices A(8,2), B(6,-4), and C(-5,-4). Find the coordinates of D.

Answer 1

Given:

ABCD is the parallelogram.

vertices are A(8,2), B(6,-4), and C(-5,-4)

We know the diagonals of the parallelogram bisect each other.

Find the midpoint of AC.

`\begin{gathered} m=((x_1+x_2)/(2),(y_1+y_2)/(2)) \\ (x_1,y_1)=(8,2) \\ (x_2,y_2)=(-5,-4) \\ m=((8-5)/(2),(2-4)/(2)) \\ m=((3)/(2),-(2)/(2)) \\ m=((3)/(2),-1) \end{gathered}`

Now, the midpoint of BD is given as,

`\begin{gathered} m=((x_1+x_2)/(2),(y_1+y_2)/(2)) \\ m=((3)/(2),-1) \\ B\mleft(6,-4\mright),D(x,y) \\ ((3)/(2),-1)=((6+x)/(2),(-4+y)/(2)) \\ (6+x)/(2)=(3)/(2),(-4+y)/(2)=-1 \\ 6+x=3,-4+y=-2 \\ x=-3,y=2 \end{gathered}`

The coordinate of D is (-3,2).