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Mass Point Geometry Help Needed Please!?
Now, I know nothing about mass point geometry so I'd like an step by step, in-depth explanation of how to answer these questions. I'm pretty sure I'm going to be using ratios somewhere but I'm not certain where and how. If anyone could help, that would be greatly appreciated. Or, you could just tell me the equation or proportion I need to start.
1. In triangle ABC, point D is a point on BA so that BD:DA = 1:2. E is a point of CB so CE: EB = 1:4. DC and AE intersect at F. Find CF:FD.
2. In quadrilateral ABCD, points E, F, G, and H are respectively in AB, BC, CD, and DA so that AE: EB = DH:HA=2:1. Point F is the midpoint of BC and CG:GD = 1:4. EG and FH intersect in K. Find HK:KF.
Um, no basic comprehension of mass point geometry whatsoever. What's sea-shaw?
And where did you get the weights from? How would you decide what the weight was for each point?
1 Answer
- TLBTHSTutoringLv 51 decade agoFavorite Answer
Haha, same question?
Same answer then. :)
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
If you have any further questions or misunderstandings, you can post them and I will try to answer them.
A: To get the weights, you have to look at the value of "other" part of that same line. The sea-shaw method is for finding the weights: If you have a heavier mass (higher number), then the "nearer part of the line" should be smaller (in value) than the other part.
It's very hard to explain this concept without visualizing it. (Sorry!)
But the following link should helps a lot!!! Again, you have to understand the concepts first to understand the solution.
www.math.utah.edu/mathcircle/2-27-08-notes-hanson-masspoints.pdf
Source(s): My knowledge of math.
