Hi there,

If I have a parallelogram, ABCD, with the following coordinates:

A(-2;3), B(4;2), C(2;-1), D(x;y) and M(0;1), which is a point in the middle of AC, determine x and y.

I know how to calculate when there is only one unknown, but not 2.

I have tried some approaches on paper, like calculating the gradient of AB, then tried to use that in the distance formula using DC coordinates...but that does not seem to do it....would someone kindly please help me with this?. Thank you all very much!

juriemagic
Sep 15, 2017

#1**+2 **

This isn't as difficult as it seems

"D" can be figured as one of three possible points

First possibility...... add A and B and subtract C....so we have

(-2 + 4 - 2, 3 + 2 - -1) = ( 0, 6) = (x,y) = D1

Second possibility....add B and C and subtract A.....so we have

(4 + 2 - -2 , 2 - 1 - 3) = ( 8, -2) = (x,y) = D2

Third possibility.....[ you might have already guessed it !! ]....add A and C and subtract B

(-2 + 2 - 4, 3 - 1 - 2) = ( -4, 0) = (x,y) = D3

If the coordinates have to follow a clock-wise order, then D3 will be the "correct" point for "D"

Here's a graph showing the possible parallelograms :

CPhill
Sep 15, 2017