Question

three of the vertices of parallelogram are ABCD and A(3,0)B(7,3)C(1,7).find the coordinate of fourth vertex D

Answer 1

In line AC, midpoint let be O(x,y)
Then,by section formula, AO:OC=1:1.
THEREFORE, coordinates of O=(nx1+mx2/m+n,ny1+my2/m+n)
(x,y)=(3+1/1+1,0+7/1+1)
=(4/2,7/2)
(2,7/2)
In Line BD, midpoint is O.
Let D be (x2, y2)
BO:OD=1:1.
THEREFORE, coordinates of O=(nx1+mx2/m+n, ny1+my2/m+n)
=(7+x2/2,3+y2/2)
Therefore, (2,7/2)=(7+x2/2,3+y2/2)
2=7+x2/2
4=7+x2
x2=-3

7/2=3+y2/2
y2=4

Therefore, D(x2, y2) =(-3,4)

HOPE THIS HELPS!!