Thread: Vector Geometry

I don't know how to approach the problem.

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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!

Originally Posted by ea22224

I don't know how to approach the problem.

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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?

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

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

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).

Did you figure out the answer...........I am trying to do the same problem...............some help and clarification would be much appreciated!!