Question

If $A(-2,2),B(8,2)$ and $C(4,-4)$ are the vertices of a parallelogram ABCD. Find the coordinates of the fourth vertex $D$ are:

• A. $(8,4)$
• B. $(6,2)$
• C. $(-8,2)$
• D. $(-6,-4)$

Answer 1

The correct option is D $(-6,-4)$

Let the vertex of $D$ be $x$ and $y.$

As we know that the diagonals of parallelogram intersect each other at point $O.$

So, it is mid-point of the line $AC$ abd $BD$

Along with $AC:$

$O_x=\frac{-2+4}{2}=1,$ $O_y=\frac{2+(-4)}{2}=-1$

Now, along with $BD,$

$O_x=\frac{8+x}{2},$ $O_y=\frac{2+y}{2}$

Now,

$1=\frac{8+x}{2}$ and $-1=\frac{2+y}{2}$

$x=-6$ and $y=-4$

$\therefore$ Co-ordinates of $D$ is $(-6,-4)$