Check is a point (x,y) is between two points drawn on a straight line

Question

I have drawn a line between two points A(x,y)---B(x,y) Now I have a third point C(x,y). I want to know that if C lies on the line which is drawn between A and B. I want to

Answer 1

ATTENTION! Math-only!

You can try this formula. Put your A(x1, y1) and B(x2, y2) coordinates to formula, then you'll get something like

y = k*x + b; // k and b - numbers

Then, any point which will satisfy this equation, will lie on your line. To check that C(x, y) is between A(x1, y1) and B(x2, y2), check this: (x1x>x2 && y1>y>y2).

Example

A(2,3) B(6,5)

The equation of line:

(y - 3)/(5 - 3) = (x - 2)/(6 - 2)
(y - 3)/2 = (x - 2)/4
4*(y - 3) = 2*(x - 2)
4y - 12 = 2x - 4
4y = 2x + 8
y = 1/2 * x + 2; // equation of line. k = 1/2, b = 2;

Let's check if C(4,4) lies on this line.

2<4<6 & 3<4<5 // C between A and B

Now put C coordinates to equation:

4 = 1/2 * 4 + 2
4 = 2 + 2 // equal, C is on line AB

PS: as @paxdiablo wrote, you need to check if line is horizontal or vertical before calculating. Just check

y1 == y2 || x1 == x2