Mass Point Geometry Problems?

To understand my solution, you should know the basic concepts of mass point (sea-shaw method) and some basic algebra skills. (Wikipedia and other websites can help you with this).

For Question 1:

1. First, you have to draw the diagram with the given information

Let say DA=2x and BD=1x. And, CE=1y and EB=4y.

2. Assign a mass to point A,B, and C.

Point C would have a mass of 4 because EB=4y. Point B would have a mass of 1 because CE=1y.

Point A would have a mass of 0.5 because point B has a mass of 1 (for AD=2x) and therefore when DB=1x (which is half of AD), the mass of the point would be half of B, which is 0.5.

Point F has a mass of 5.5 because the mass of point A+E = 5.5 and C+D=5.5 also.

3. Now you just have to look at the line CD. CF:FD would be 1.5: 4 ;CF with the point D(mass: 1.5)) and FD with the point C (mass: 4).

CF:FD= 1.5:4= 3:8

ANSWER: 3:8

For question 2:

1.First, you have to draw the diagram with the given information.

Let say: AE=2x, EB=1x, BF=1z, FC=1z, CG=1a, GD=1a, DH=2y, and HA=1y.

2.Assign masses to points A,B,C, and D by the same logic as number 1: A=2, B=4, C=4, and D=1.

Point H = 3 because you have to add the masses of point A (2) and point D(1): 2+1=3.

Point F =8 because you have to add the masses of point B (4) and point C(4): 4+4=8.

3. It is now pretty clear (I hope) that HK:KF=8:3 ; HK with the point F (mass of 8) and KF with the point H (mass of 3).

ANSWER:8:3