Question

three vertices of parallelogram EFGH are E(4,2),F(7,3),and H(5,4).Find the coordinates of vertex G.

Answer 1

Using the midpoint of the diagonals ,since the diagonals bisect each other:

Midpoint of ef((4+7)/2 ; (2+3)/2)
Midpoint of ef(5.5 ; 2.5)
therefore: Midpoint of hg((5+x)/2 ; (4+y)/2)
(5+x)/2=11/2 and 4+y=5/2
5+x=11 and 4+y=5
x=6 and y=1
G(6;1)