How can I tell if a point belongs to a certain line?
Examples are appreciated, if possible.
In the simplest form, just plug the coordinates into the line equation and check for equality.
Given:
Point p (X=4, Y=5)
Line l (Slope=1, YIntersect=1)
Plug in X and Y:
Y = Slope * X + YIntersect
=> 5 = 1 * 4 + 1
=> 5 = 5
So yes, the point is on the line.
If your lines are represented in (X1,Y1),(X2,Y2) form, then you can calculate slope with:
Slope = (y1 - y2) / (x1-x2)
And then get the Y-Intersect with this:
YIntersect = - Slope * X1 + Y1;
Edit: I fixed the Y-Intersect (which has been X1 / Y1 ...)
You'll have to check that x1 - x2
is not 0
. If it is, then checking if the point is on the line is a simple matter of checking if the Y value in your point is equal to either x1
or x2
. Also, check that the X of the point is not 'x1' or 'x2'.