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

- anonymous

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

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- schrodinger

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- anonymous

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- phi

the medians are divided by the centroid into the ratio of 2/3 to 1/3

- anonymous

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

- anonymous

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)

- anonymous

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 ?

- anonymous

I get that the long side is SU and ST and UT

- anonymous

I get it now!!

- anonymous

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

- anonymous

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

- anonymous

(2*2 - 1) 10
1x = 10
x= 10

- phi

do you see the "length" of XY ?

- anonymous

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 ?

- anonymous

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)

- anonymous

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

- anonymous

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.

- anonymous

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.

- anonymous

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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