My Math Forum Formula to determine value of Y in a triangle

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 December 25th, 2013, 04:24 PM #1 Newbie   Joined: May 2013 Posts: 6 Thanks: 0 Formula to determine value of Y in a triangle Hello folks, I'm trying to make a script that calculates the coordinates at a specific point of a triangle vertex. But I've looked every where and wasn't able to understood how to do it. So I need someone to explain a formula to find the value of these coordinates, given this example: http://img703.imageshack.us/img703/1694/l8o6.png I always have the value of X, but I need just to discovery the value of Y on this graphic. Thanks for your attention.
 December 25th, 2013, 04:28 PM #2 Member   Joined: Feb 2013 Posts: 80 Thanks: 8 Re: Formula to determine value of Y in a triangle Are you looking just for the linear equation of the hypotenuse of that triangle?
 December 25th, 2013, 04:33 PM #3 Newbie   Joined: May 2013 Posts: 6 Thanks: 0 Re: Formula to determine value of Y in a triangle To be honest, I don't know. If this equation gives me the value of Y, yes, I am...
December 25th, 2013, 05:18 PM   #4
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Re: Formula to determine value of Y in a triangle

Quote:
 Originally Posted by afonsolage Hello folks, I'm trying to make a script with calculates the coordinates at a specific point of a triangle vertex. But I've looked every where and wasnt able to understood how to do it. So I need someone to explain a formula to find the value of this coordinates, given this example: http://img703.imageshack.us/img703/1694/l8o6.png I always have the value of X, but I need just to discovery the value of Y on this graphic. Thanks for your attention.
Shouldn't the far right lower coordinate be (-6.1,1.0)?

You want to find the line equation of the hypotenuse in the form

$y=mx+c$

First of all find the gradient of the hypotenuse

$\frac{2.2-1.0}{-6.1-(-10.0)}=\frac{1.2}{3.9}=\frac{4}{13}$

So now we have:

$y=\frac{4}{13}x+c$

Now we use one of the coordinates we know, say (-10.0,1.0) and substitute them in our equation:

$1.0=\frac{4}{13}(-10.0)+c$

and solve for c.

$c=\frac{53}{13}$

Thus our line equation for the hypotenuse is:

$y=\frac{4}{13}x+\frac{53}{13}$

We now enter the x-coordinate we have to find the y-coordinate we don't know from (-8.0,y):

$y=\frac{4}{13}(-8.0)+\frac{53}{13}=\frac{21}{13}\simeq1.6$ (to 1 d.p.)

So our missing coordinate is (-8.0,1.6)

 December 25th, 2013, 07:30 PM #5 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 10,904 Thanks: 716 Re: Formula to determine value of Y in a triangle From similar triangles: k/2 = 1.1/3.9 k = ~.564 So y coordinate = 1 + .564 = 1.564 = 1.6 rounded
 December 26th, 2013, 01:58 AM #6 Global Moderator   Joined: Dec 2006 Posts: 18,154 Thanks: 1418 With Slinkey's correction, k = (2.2 - 1.0)(10.0 - 8.0)/3.9 = 8/13, so Y = 1 + k = 21/13 = 1.615... .
 December 26th, 2013, 04:06 AM #7 Newbie   Joined: May 2013 Posts: 6 Thanks: 0 Re: Formula to determine value of Y in a triangle First of all, thanks for all replies, I've learn many things today, second, sorry for my mistake, the far right lower coordinate should be (-6.1,1.0). But I have some questions: 1 - Slinkey, I didn't understood how 1.0 = 4/13*(-10.0)+c, became c=53/13. Let me show what I'm thinking: 1.0 = 4/13*(-10.0)+C C = (4/13*(-10/1)) => (4*-10)/(13*1) C = -40/13 2 - Denis, how you got the 1.1 value? This is the wrong Y value I've posted? So, the right one should be 1.0/3.9? But, this is how I can represent this as a formula? Given A(-10.0, 1.0), B(-6.1, 1.0), C(-6.1, 2.2), P(-8.0, 1.0) and Q(-8.0, Y), I have: K/2 = Cy-By/Cx-Ax, so Y = Py+K 3 - Skipjack, I need to use some Modulus, or any value can be negative? Using the below formula I got a different result, is it right? Given A(-10.0, 1.0), B(-6.1, 1.0), C(-6.1, 2.2), P(-8.0, 1.0) and Q(-8.0, Y), I have: K = (Cy-By)*(|Ax|-|Px|)/|Ax|-|Cx|, so Y = Py+K. Sorry, if I look silly, but I'm really trying to understand this and create a script formula to calculate this Y, given any value on A, B, C and P.
December 26th, 2013, 10:36 AM   #8
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Re: Formula to determine value of Y in a triangle

Quote:
 Originally Posted by afonsolage 2 - Denis, how you got the 1.1 value? This is the wrong Y value I've posted? So, the right one should be 1.0/3.9? But, this is how I can represent this as a formula? Given A(-10.0, 1.0), B(-6.1, 1.0), C(-6.1, 2.2), P(-8.0, 1.0) and Q(-8.0, Y), I have: K/2 = Cy-By/Cx-Ax, so Y = Py+K
Yes; I didn't notice your slight error in posting; was on my 1st coffee...Slinky for sure was on his 2nd !

So we have right triangle ABC:
AB = -6.1 - (-10) = 3.9
BC = 2.2 - 1 = 1.2
And right triangle APQ:
AP = -8 - (-10) = 2
PQ = y - 1

The 2 triangles are SIMILAR, so:
AB / BC = AP / PQ
3.9 / 1.2 = 2 / (y-1)
Solve to get y = 1.61538...as per Slinky and Skip.

I originally use k to represent y-1; that was just my way...no need to do so...

IF you're learning about right triangles and similar triangles, then your teacher
was sure in NO Xmas mood when picking that "confusing" example

 December 26th, 2013, 10:54 AM #9 Newbie   Joined: May 2013 Posts: 6 Thanks: 0 Re: Formula to determine value of Y in a triangle @Denis, Thanks for the reply, I've understood now. This example wasn't given by my teacher, because I'm 24 years old and skipped those lessons at school (big mistake). This was a real example of an application I'm developing and I got stuck on this formula, but not any more
 December 26th, 2013, 11:27 AM #10 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 10,904 Thanks: 716 Re: Formula to determine value of Y in a triangle Alfonso, in case I confused you by not using coordinates, I was using a short-cut by calculating the side lengths separately... However, I notice that you're looking for a "method/formula" using the given coordinates, in order to handle any given coordinates; SO: Code: B(Bx,By)[2,12] Q(Qx,Qy)[6,?] C(Cx,Cy)[2,3] P(Px,Py)[6,3] A(Ax,Ay)[14,3] Above is an easier example; I'm showing the GIVENS in [square brackets]. As in your original example, we need to calculate Qy. BC / AC = QP / AP (By - Cy) / (Ax - Cx) = (Qy - Py) / (Ax - Px) Qy = [(By - Cy)(Ax - Px)] / (Ax - Cx) + Py Qy = [(12 - 3)(14 - 6)] / (14 - 2) + 3 Qy = 9 Note that in actual practice/programming, you'd use the ABSOLUTE results of above subtractions... However, I'm sure you were aware of all that stuff...

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