Posted by Jat on .
Triangle ABC with D, E and F the midpoints of BC, AC, and AB. G is the midpoint of AD such that the ratio AG:GD =2:1, VECtors AB =p and BC =q
Prove that B, G and E are collinear. prove the same results for point C, G and F

Advanced Maths (Vectors) AQA Level 
Reiny,
Something is not right here, ....
If D is the midpoint of BC , then AD is clearly a median
you then say, G is the midpoint of AD such that
AG:GD = 2:1
From the 2:1 ratio we know that G must be the centroid, which of course cannot be the midpoint.