Given that Y is the centroid of triangle STU, find X. I added 2x - 3 + 10 = 180

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Given that Y is the centroid of triangle STU, find X. I added 2x - 3 + 10 = 180

Mathematics
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  • phi
the medians are divided by the centroid into the ratio of 2/3 to 1/3
So they are equal, I'm thinking..

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  • phi
in other words, the "long side" is 2 times bigger than the "short side" here the long side is 10 and the short side is 2x-3
Oh, I think I get it now.. so it's 2(20)-3
  • phi
re-think that. long side is 2 * short side replace "long side" with 10 replace "is" with = replace "short side" with (2x-3)
oh okay, now I think it is 2 times 10 minus 3..
  • phi
can you do each of these steps: long side is 2 * short side replace "long side" with 10 replace "is" with = replace "short side" with (2x-3) can you do that ? what do you get ?
I get that the long side is SU and ST and UT
I get it now!!
9 is the short side, 9 times 2 is 18. 18 minus 3 is 15.
  • phi
oh. we are talking about the median line XT which is divided by the point Y the short side is XY and the long side is YT
  • phi
in other words, the median XT is what is divided into two parts, where the short part is 1/2 of the longer part
Aw, I thought I did it right..
  • phi
we want to find x so we concentrate on just the median XT it can be proved that 2* XY = YT
  • phi
so we start with 2* XY = YT and "put in" the info they give us about the length of XY and the length of YT
(2*2 - 1) 10 1x = 10 x= 10
  • phi
do you see the "length" of XY ?
well XT = 10, and XY is half of XT, so XY=5 ?
  • phi
yes, that is good thinking. but according to the label in your picture XY is also what ?
Umm, X is the centroid but I'm not exactly sure what Y is..
  • phi
XY is way to say, "the line segment joining X to Y"
  • phi
and that line segment from X to Y has a label in your picture
  • phi
in other words, they say the length of XY is (2x-3)
Thank you for all the help @phi I completely set up the equation wrong until you explained it to me!
  • phi
using XY=5 (which you figured out up above) you can write 2x-3 = 5 and now "solve for x"
  • phi
If I were doing it I would write 2*XY= YT then replace XY with (2x-3) and YT with 10 to get 2(2x-3)= 10 then solve for x if we divide both sides by 2 as the first step, we get 2x-3= 5 now add +3 to both sides 2x-3+3= 5+3 2x= 8 and finally divide both sides by 2
When multiple numbers are given to me in diagrams I get so confused as to what to add, usually I start plugging in my options into the equations. Sometimes it works, sometimes it doesn't. Thank you again, it really did make sense when it was explained to me :)
  • phi
sorting out what info to use is the hard part. If you get good at that, then you will get good at thinking in general, and that is why you are studying math.
You're definitely right. I've been struggling with math all through high school. It's not even that I don't try, it's that I get so confused. I have to draw separate images sometimes (for triangles)
  • phi
You can learn this, but it takes lots of work to learn how to tackle a problem. If I get confused and later get the answer I go back and ask, "why did I not see how to do it?" what was I not thinking? or thinking wrong? and then: if I see a problem like this again, "what will I do?" hopefully I will learn how to do the problem correctly.
I totally agree with you, this sounds crazy, but when a math problem has multiple numbers and equations, I actually get stressed out..

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