SOLUTION: The points (5,2), (2,6), and (-8,-3) are three vertices of a parallelogram. Locate and give the coordinates of a fourth vertex. Find all possible solutions.

Question 52904: The points (5,2), (2,6), and (-8,-3) are three vertices of a parallelogram. Locate and give the coordinates of a fourth vertex. Find all possible solutions.
Found 2 solutions by venugopalramana, bwpbruce:
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
The points A=(5,2), B=(2,6), and C=(-8,-3) are three vertices of a parallelogram. Locate and give the coordinates of a fourth vertex. Find all possible solutions.
WE USE THEPRINCIPAL THAT DIAGONALS OF A PARALLELOGRAM BISECT EACH OTHER.
IF ABCD IS THE PARALLELOGRAM AND D IS (H,K) THEN
MID POINT OF AC = [{(5-8)/2=-3/2},{(2-3)/2=-1/2}]=(-1.5,-0.5)=MID POINT OF BD =
=[(2+H)/2,(6+K)/2]
2+H=-1.5*2=-3....H=-5
6+K=-0.5*2=-1.....K=-7
D IS (-5,-7)
IF ACBD IS THE PARALLELOGRAM THEN D IS GIVEN BY
MIDPOINT OF AB IS = (7/2,8/2)= MID POINT OF CD = H-8/2,K-3/2
H-8=2*7/2=7.......H=15
K-3=2*8/2=8..........K=11
HENCE D IS (15,11)
Answer by bwpbruce(7) (Show Source): You can put this solution on YOUR website!

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