At min 3:00,shouldn't it be x+4x = 5?I mean,you are changing the pivot point to BT/TE and the weight at is (a + b)=x+4x.also ,if you are to add the lenghts shouldn't it be BT + TE =4 +1=5?
This is because we already established arbitrary weights in the first step. After that, we cannot just use random weights, or else it might contradict our previous designation. For example, if we just used 1 and 4, then the weight on T would both be 4 (from A+D) and 5 (from B+E) which is impossible.
I don’t think I’m right and I’m probably late, but I don’t think it matters about the line segments for the middle point, only the endpoints of the line.
![Mass Point Geometry Part 2 [AIME 1 2009 #4]](http://i.ytimg.com/vi/_5IrxEJADQ0/mqdefault.jpg)
![Mass Point Geometry Part 2 [AIME 1 2009 #4]](/img/tr.png)
Yay I learned something!
At min 3:00,shouldn't it be x+4x = 5?I mean,you are changing the pivot point to BT/TE and the weight at is (a + b)=x+4x.also ,if you are to add the lenghts shouldn't it be BT + TE =4 +1=5?
+Tore Chikano I have the same question. Can anyone help
We had already calculated the weight of T to be 4, from the addition of A and D. Since T=B+E, it follows that 4=x+4x. Does this make sense?
+Cyclic Squares I am kinda confused on why you have to use x and 4x why are you not allowed to just add real weights such as 1 and 4
This is because we already established arbitrary weights in the first step. After that, we cannot just use random weights, or else it might contradict our previous designation. For example, if we just used 1 and 4, then the weight on T would both be 4 (from A+D) and 5 (from B+E) which is impossible.
+Cyclic Squares oh makes sense. Thanks man
I need to learn how to not spit in the microphone *shame*
Why do all the Daniel Liu's I know are good at math
Thank you!!
Dude, your a bloody legend. I actually made chapter countdown. YaY!
Math DUDE I made states lol but choked there
congrats!
So I pretend that the triangle is a bunch of seesaws?
And do those numbers as weights REALLY exist?
Yep, pretend that each line segment is a see saw.
As for your second question, I'm not sure what you mean by "exist". Do numbers in general exist?
Cyclic Squares im too tired for this right now...
FireShell7 Do you need any help, or do you just need a cup of coffee?
Cyclic Squares coffee, although I already aced the final thanks to this!
Good job! I'm inclined to ask, what finals are you taking? Mass Points Geometry usually does not occur in school math.
Thanks!
Question: shouldn't it be x+4x = 5, since the sum of the lengths is 5?
Newtonian No, the two weights add up to the weight in the middle, at point T
I didn't understand how C is 11/5; doesn't that provide AE=EC=1 because A=1 and E=16/5, if C=11/5 then E=1.A+1.C
I don’t think I’m right and I’m probably late, but I don’t think it matters about the line segments for the middle point, only the endpoints of the line.
damn daniel thanks man
Are there any proofs that this technique works?
Samuraiwarm Tsunayoshi This might help: math.stackexchange.com/questions/75868/how-to-prove-we-could-use-mass-point-geometry-to-solve-all-the-triangle-problem
Menelaus
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