Find Coordinates of Collinear Point

Question

Hey, so I'm trying to get the coordinates Y of the third colinear point in javascript

so like in this example we're trying to find the Y coordinate of P3.

I wrote a small code :

p1 = {
  x: -6,
  y: -9
}

p2 = {
  x: 3,
  y: -3
}


p3 = {            
  x: 12
}

a = p2.y - p1.y
b = p2.x - p1.x
slob = a/b

b = -(slob*p2.x - p2.y)

y = slob*p3.x + b

p3.y = y

console.log(p3)

// checks if its correct
var a = p1.x * (p2.y - p3.y) + p2.x * (p3.y - p1.y) + p3.x * (p1.y - p2.y);

if (a == 0){
  console.log("correct")
} else {

  console.log(a, 'incorrect')
}

But weirdly it only works for this concrete example.

Does anybody has any ideas of how to do that or what am I doing wrong

Thank you in advance

What's the logged value of `a`? – raina77ow Jul 03 '21 at 22:08 — raina77ow, Jul 03 '21 at 22:08

raina77ow · Answer 1 · 2021-07-03T23:10:22.360

The key idea of the solution is that the ratio of the sides stays the same. In other words,

(p2.y - p1.y) / (p2.x - p1.x)

... which is stored as slob in your code, should be equal to both:

(p3.y - p2.y) / (p3.x - p2.x) // shoulders
(p3.y - p1.y) / (p3.x - p1.x) // big triangle

Now, your code attempts to calculate the missing value (p3.y) based on the first of those. There's a lot of reassigning different values to the same variables (which is a bad practice btw), but in the end it boils down to this equation:

p3.y = slob * (p3.x - p2.x) + p2.y

... which is algebraically correct. Now, the checking expression uses 'big triangle' formula, which can be simplified to this:

p3.x * (p2.y - p1.y) = p1.x * (p2.y - p3.y) + p2.x * (p3.y - p1.y)

Your real problem here is that two approaches - the 'solution' one and the 'checker' one - are different in how they use floating-point math. The checking expression substracts and multiplies its operands, but there's never a case of division there.

It's not like that, however, with 'solution' approach. In the given example, slob is 6 / 9 - which means it can be stored only with a certain level of precision in JavaScript.

Now, sometimes you get lucky - and the stored value's precision is enough. But sometimes it's snake eyes, like in this infamous example:

0.3 === 0.2 + 0.1 // false

... and you actually get slightly incorrect result stored in p3.y, which is enough to tip the scales of checker equation.

Find Coordinates of Collinear Point

1 Answers1