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If you have the $X$ and $Y$ coordinates for $2$ lines on a $2D$ plane/graph is it possible to detect via true/false if they cross paths? I'm just trying to detect if lines are not parrallell.

If $(X,Y)$ is $(20, 20)$ to $(X_2,Y_2)$ of $(30,30)$ and a second line is $(X_3,Y_3) (18,22)$ to $(X_4,Y_4)$ of $(30,25)$.

Shubham Johri
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DaveyBoy85
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1 Answers1

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$2$ non-parallel lines will always intersect. If the lines are parallel, they may or may not be coincident.

For a straight line, its slope $m=\frac{y_2-y_1}{x_2-x_1}$, where $(x_1,y_1),(x_2,y_2)$ are two distinct points on the line, describes how the line is inclined with respect to the $x$ axis. The slopes of two parallel lines are equal and unequal for non-parallel lines.

So, you will have to find the slope of the lines. If they are unequal, they intersect at a unique point. Otherwise, the lines are parallel. If, then, they are coincident, the slope of the line joining any point on one line and any point on the second line is equal to the slope of either line. If that's not the case, they don't intersect.

Shubham Johri
  • 17,659
  • So in the case in the original post its 10/10 and -12/-3. So since unequal theres a definite intersect between them? – DaveyBoy85 Dec 17 '18 at 20:36
  • Yes. Well, the slope of the second line is $3/12$, but that doesn't matter because if the slopes are unequal, so are their reciprocals. You should read more about straight lines and their slopes online. – Shubham Johri Dec 17 '18 at 20:39