# Vector Geometry

• Jan 3rd 2013, 02:02 PM
ea22224
Vector Geometry
I don't know how to approach the problem.
Draw triangle ABC, with P the midpoint of AB, Q the midpoint of BC, and R the Midpoint of CA. If X is any point , show that XA + XB + XC = XP + XQ + XR
Thanks!
• Jan 3rd 2013, 02:08 PM
Plato
Re: Vector Geometry
Quote:

Originally Posted by ea22224
I don't know how to approach the problem.
Draw triangle ABC, with P the midpoint of AB, Q the midpoint of BC, and R the Midpoint of CA. If X is any point , show that XA + XB + XC = XP + XQ + XR
Thanks!

This is a nice question. What have you done towards solving?
It can teach you a great deal.
So post what you have done?
• Jan 15th 2013, 03:19 PM
ea22224
Re: Vector Geometry
so i wrote that XP = XA + AP and XP = XB - PB
AP = PB so i combined the two equations to ge 2XP = XA + XB
and that 2XR = XA +XC and 2XQ = XB + XC
adding the three equations together, i got 2XA +2XB + 2XC = 2XP + 2 XR + 2XQ and then simplified.
Am I doing it right, or did i miss something
• Jan 15th 2013, 04:23 PM
HallsofIvy
Re: Vector Geometry
I think I would be inclined to start with the obvious: AB+ BC= AC. Then divide both sides by 2.
• Jan 15th 2013, 08:35 PM
richard1234
Re: Vector Geometry
Edit: Whoops, I might have misinterpreted vectors as lengths of segments (if XA referred to the length of XA, as opposed to vector XA, the problem would be clearly flawed).
• May 5th 2013, 11:10 AM
maliwalters
Re: Vector Geometry
Did you figure out the answer...........I am trying to do the same problem...............some help and clarification would be much appreciated!!