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December 25th, 2013, 03:24 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, 03:28 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, 03:33 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, 04:18 PM  #4  
Member Joined: Dec 2013 Posts: 82 Thanks: 0  Re: Formula to determine value of Y in a triangle Quote:
You want to find the line equation of the hypotenuse in the form First of all find the gradient of the hypotenuse So now we have: Now we use one of the coordinates we know, say (10.0,1.0) and substitute them in our equation: and solve for c. Thus our line equation for the hypotenuse is: We now enter the xcoordinate we have to find the ycoordinate we don't know from (8.0,y): (to 1 d.p.) So our missing coordinate is (8.0,1.6)  
December 25th, 2013, 06:30 PM  #5 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038  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, 12:58 AM  #6 
Global Moderator Joined: Dec 2006 Posts: 20,919 Thanks: 2203 
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, 03:06 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 = CyBy/CxAx, 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 = (CyBy)*(AxPx)/AxCx, 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, 09:36 AM  #8  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038  Re: Formula to determine value of Y in a triangle Quote:
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 / (y1) Solve to get y = 1.61538...as per Slinky and Skip. I originally use k to represent y1; 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, 09:54 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, 10:27 AM  #10 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038  Re: Formula to determine value of Y in a triangle
Alfonso, in case I confused you by not using coordinates, I was using a shortcut 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] 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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