Question

A(-1, 0) B(3 ,1) and c( 2,2) are the vertices of a parallelogram ABCD. The coordinates of the fourth vertex D is​

Answer 1

Explanation:

Let A(−1,0), B(3,1),C(2,2) and D(x,y) be the vertices of a parallelogram  ABCD taken in order. Since the 

diagonals of a parallelogram bisect each other.

∴ Coordinates of the mid point of AC

=Coordinates of the mid point of BC

⇒(2−1+2,20+2)=(23+x,21+y)

⇒(21,1)=(23+x,2y+1)

⇒23+x=21 and 2y+1=1

⇒x=−2 and y=1

Hence the fourth, vertex of the parallelogram is   (−2,1)