Question

If A(-2,-1),B(x,0),C(4,y) and D(1,2) are the vertices of a parallelogram, taken in order, find x and y. also, find the area of the parallelogram ABCD

Answer 1

the mid point of the diagonals of parallelogram is same.
(-2+4/2,-1+y/2)=(x+1/2.,0+2/2)
after solving we get x=1,y=3
area of parallelogram is 1/2 × length of diagonal 1 ×length of diagonal 2
1/2×AC×BD