1. ## 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!

2. ## Re: Vector Geometry

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?

3. ## 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

4. ## Re: Vector Geometry

I think I would be inclined to start with the obvious: AB+ BC= AC. Then divide both sides by 2.

5. ## 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).

6. ## 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!!