Checking if a Point is on a Line - Jay's Query

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To determine if a third point is on a line defined by two points on a Cartesian plane, compare the slopes of the segments formed by the points. If the slope between the first two points (p1 and p2) is equal to the slope between either of the first two points and the third point (p3), then all three points are collinear. This method can be implemented in programming for game development to validate user input. Ensuring accurate slope calculations will allow for effective checking of the point's position relative to the line. This approach is essential for enhancing user interaction in the game.
inadaze
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Hey,
I was wondering:
If I had two points connected by a line on a cartesian plane(x and y for this) and i wanted to draw a third point, how could i tell if the third point was drawn somewhere on the line? I am programing a game where there is already a line drawn to connect to points and the user is supposed to draw a third point. i want to be able to check if it was drawn on the line or not.

Thanks
Jay
 
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Let p1 and p2 be the original two points, and p3 the third point. If the slopes between p1 and p2 is equal to that between p1 and p3 (or p2 and p3), then the three points lie on the same line.
 

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