Author 
Topic 

uberclay
Advanced Member
Canada
159 Posts 
Posted  04/16/2012 : 23:53:43

Given the parallelogram ABCD, where A (4, 2), B (6, 1) and D (3, 4), find the coordinates of C.
I cannot, for the life of me, wrap my head around this problem. Initially I solved this by observation (B is to A as C is to D) for the solution C (13, 5), but it's supposed to be solved using Vector addition/subtraction.
The Cartesian Vectors I get are AB (10, 1) and AD (7, 6) giving magnitudes AB = 101^(1/2) and AD = 85^(1/2)
I found the angle between AB and AD by 90°  tan^1 (1/10) + tan^1 (7/6) (this is a predot/cross product lesson)
The cosine law gives the correct magnitude for the diagonal AC; AC = AB + AD = AB^2 + AD^2  2ABADCos, where = 180  BAD, which is 338.
And here is where I am stuck. How do I get the coordinates out of this magnitude? 


uberclay
Advanced Member
Canada
159 Posts 
Posted  04/17/2012 : 13:36:16

Disregard. I have hugely overcomplicated this.
All that needs to be done here is vector addition I'll work it out and let you know how it goes. 
Edited by  uberclay on 04/17/2012 14:14:33 


uberclay
Advanced Member
Canada
159 Posts 
Posted  04/17/2012 : 19:08:13

I'm still baffled but I think I got it.
Subtracting the vector OA from OB gives AB = (10, 1)
And adding the vector OD to AB gives OC
AB + OD = (10, 1) + (3, 4) = (13, 5)
Therefore C = (13, 5)
I couldn't find an example in the text, which is odd. And my submitted answer (graded as incorrect) was the same logic without the vector notation.
I'm assuming that evaluating for AB establishes the relation between A and B, and when applied to D, gives the location of C. 
Edited by  uberclay on 04/17/2012 19:41:33 


Ultraglide
Advanced Member
Canada
299 Posts 
Posted  04/17/2012 : 22:02:40

You're making this way too hard. The coordinates of a parallelogram, if they are given as letters, are always cyclic so in this case AB is parallel to DC. Now vector AB is (64, 12) or (10,1). Let C have coordinates (x,y) so DC is (x(3), y(4)) or (x+3, y+4). But AB and DC are equal so x+3=10 giving x = 13 and y+4=1 giving y = 5. So (x,y)=(13, 5). You can check as follows,  13  (3) = 10 and 5 (4) = 1. 


uberclay
Advanced Member
Canada
159 Posts 
Posted  04/18/2012 : 16:56:27

Well, it makes sense now ; 0 )
Thanks Ultraglide 



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