## Question

Asked By – Paul D. Eden

Let’s say you have a two dimensional plane with 2 points (called a and b) on it represented by an x integer and a y integer for each point.

How can you determine if another point c is on the line segment defined by a and b?

I use python most, but examples in any language would be helpful.

**Now we will see solution for issue: How can you determine a point is between two other points on a line segment? **

## Answer

Check if the **cross product** of (b-a) and (c-a) is 0, as tells Darius Bacon, tells you if the points a, b and c are aligned.

But, as you want to know if c is between a and b, you also have to check that the **dot product** of (b-a) and (c-a) is *positive* and is *less* than the square of the distance between a and b.

In non-optimized pseudocode:

```
def isBetween(a, b, c):
crossproduct = (c.y - a.y) * (b.x - a.x) - (c.x - a.x) * (b.y - a.y)
# compare versus epsilon for floating point values, or != 0 if using integers
if abs(crossproduct) > epsilon:
return False
dotproduct = (c.x - a.x) * (b.x - a.x) + (c.y - a.y)*(b.y - a.y)
if dotproduct < 0:
return False
squaredlengthba = (b.x - a.x)*(b.x - a.x) + (b.y - a.y)*(b.y - a.y)
if dotproduct > squaredlengthba:
return False
return True
```

This question is answered By – Cyrille Ka