我如何才能知道一个点属于某一行？

How can I tell if a point belongs to a certain line?

例子是AP preciated，如果可能的话。

Examples are appreciated, if possible.

推荐答案

在最简单的形式，只需将坐标转换为直线方程，并检查是否相等。

In the simplest form, just plug the coordinates into the line equation and check for equality.

由于：

Point p (X=4, Y=5)
Line l (Slope=1, YIntersect=1)

插上X和Y：

Plug in X and Y:

   Y = Slope * X + YIntersect
=> 5 = 1 * 4 + 1
=> 5 = 5

所以，是的，一点就行了。

So yes, the point is on the line.

如果您的线条被重新psented在$ P $（X1，Y1），（X2，Y2）的形式，那么你就可以计算出斜率为：

If your lines are represented in (X1,Y1),(X2,Y2) form, then you can calculate slope with:

 Slope = (y1 - y2) / (x1-x2)

，然后得到的Y相交的：

And then get the Y-Intersect with this:

 Y-Intersect = - Slope * X1 + Y1;

编辑：我固定的Y相交（已经进行了X1 / Y1 ...）

I fixed the Y-Intersect (which has been X1 / Y1 ...)

您将必须检查 X1 - X2 不是 0 。如果是，则检查是否点上线检查，如果你点的Y值等于或者 X1 或 X2 。此外，检查点的X不是X1或X2。

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'.