Parallelograms and Vectors
“Again with the maths…” Thursday on the train home, I was trying to solve a maths exercise - I am given A, B and C. I was asked to solve D so that ABCD formed a parallelogram. Where did I start? Here’s what I originally thought:
- kBC = AD (The top and bottom edges should be parallel)
- |AB| = |CD| (The two sides would be the same length)
I couldn’t think of any more rules to help me, so I gave made a note of it, then moved on. It wasn’t long until I’d be at it again, and this time I’d solve it.
Paul (again) mentioned that you could use the midpoint between the opposing vertices (A and C ) and (B and X). And that’s how I solved it 
Here is the proof…
If A, B and C are known, solve D so ABCD forms a parallelogram.
Mathamatical Methods for Engineers and Scientists, p7, 1.2.3 Q3
Blast my inferior logic!
Tags: geometry, logic, midpoint, parallelogram, solution, vectors