Math Is Fun Forum / Vector Proof Question

kevi555 · 2005-11-30 15:10:50

Hi...

For this question you have to prove it by using vector methods.

Q: Prove that medians AD and BE of triangle ABC intersect at a point that divides each median in the ratio 2:1.

Any help would be greatly appreciated.

Thanks

tz · 2005-12-04 12:09:27

OD = 1/2OB + 1/2OC
Let CF be the other median.

Prove that AD and BE's intersection, G divides AD in the ratio of 2:1.

Proof:

OD = 1/2OB + 1/2OC
OF = 1/2OA + 1/2OB

OD - OF = 1/2OC - 1/2OA
OD + 1/2OA = OF + 1/2OC
2OD + OA = 2OD + OC
2/3OD + 1/3OA = 2/3OF + 1/3OC
OG = OG

Ads

Menu

#1 2005-11-30 15:10:50

Vector Proof Question

#2 2005-12-04 12:09:27

Re: Vector Proof Question

Board footer