Dot product problem

May 2010
2
0
Ok heres the question i am stuck on. I have tried many things and can't get it.

The points P(-2,1),Q(-6,4),and R(4,3) are three vertices of parrallelogram PQRS
a) Find the coordinates of S
 
Apr 2010
384
153
Canada
Ok heres the question i am stuck on. I have tried many things and can't get it.

The points P(-2,1),Q(-6,4),and R(4,3) are three vertices of parrallelogram PQRS
a) Find the coordinates of S
You don't need to use the dot product here, in fact, all we need to do is construct the diagram.

This is what our diagram should look like: Parallelogram - Wikipedia, the free encyclopedia

So graph the points you have and label the remaining point in the vacent corner S and draw lines to it.

The height of the known side (point Q to point P) is \(\displaystyle 4-1 = 3 \) and the right side of the diagram has point R at height 3. We know that, by the shape of the parallelogram S needs to be bellow R, so its height or y co-ordinate is \(\displaystyle 3-3=0 \)

The same procedure but for the x-cordinate between R and Q yields \(\displaystyle -6-4 = -10 \). Thus, the x co-cordinate for S is \(\displaystyle -2 - - 10 = 8 \)

S is at (8, 0)
 

CaptainBlack

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Ok heres the question i am stuck on. I have tried many things and can't get it.

The points P(-2,1),Q(-6,4),and R(4,3) are three vertices of parrallelogram PQRS
a) Find the coordinates of S
Treating as 2-vectors:

PQ=Q-P

QR=R-Q

RS=S-R

But this is a paralleogram so RS=-PQ hence:

S=R-PQ=R-Q+P

CB