Harmeed

Hello everyone... It's me again...The young student who you always help and thanks to you all I'm improving in math calculations and reasoning ability.... Thank you all. I would like to give thanks to "skipjack"[by username] who has always been there for me.
...and referring to my last post that post help me a lot... and I really appreciate everyone who contributed to the post it really help me... Now, I have another question if you won't mind...
The equations of sides AB,BD and AD of a parallelogram ABCD are y-x+1=0, y+2x-11=0 and y-4x+7=0 respectively. Find the coordinates of A,B,C,D
...
I have obtained some coordinates by performing simultaneous equation for
D(3,5)
A(2,1)
B(4,3)
To find C coordinates, according to the diagram I drew,
since
CB is perpendicular to AB so using m2=-1/m1 I obtain the slope of CB inserting the coordinates of B, I obtained y+x=7.
Doing the same thing for CD, which is perpendicular to AD, and inserting D coordinates, I obtained 4y+x=23.
After picking both equations and solve, I obtain a wrong answer.

skipjack

As ABCD is a parallelogram, you can't assume that CB is perpendicular to AB.

As the diagonals AC and BD bisect each other, adding corresponding coordinates of B and D must give the same results as adding corresponding coordinates of A and C.

Adding the coordinates of B and D gives (7, 8).
Subtracting the coordinates of A from that gives C as the point (5, 7).