Consider this problem

AE:EB=2:3, AD:DC=4:7

Determine BP:PD

SOLUTION: We will use a method called “MASS POINTS”. Assign a mass (weight) of 2x, 3x,4y and 7y to respectively. Think about balance. To be balanced at E, A needs a weight of 3x and B a weight of 2x. To be balanced at D, A needs a weight of 7y and C needs a weight of 4y. So, at A, 3x=7y. Pick any nice solution. X=7, y=3 works. Plug it back in. B has a mass of 14, A a mass of 21 and C a mass of 12. So, to be balanced, D has to have a mass of 21+12=33 – All mass must be centralized. Since B ahs a mass of 14, BP:PD=33:14 and we are done.

Problem 1 You find EP:PC in the problem above.

2) KW:WF=3:5, FN:NM=1:4 Find WR:RM & KR:RN

3)

PT:TD=4:5 DS:SQ=3:2

Find TV:VQ and VS:PV

4) In DABC, D lies on so that AD:DB=3:8, E lies on so that AE:EC=4:9 and F is the intersection of . Find DF:FC and EF:FB

5) and are medians of DGIJ. Determine HL:LJ and KL:LI