Question: I have two points `A (x1,y1)` and `B (x2,y2)` that are given as an input to the program. I have to find a third point `C` that lies on the line `AB` and is at a distance `10` away from the point A.

I can easily get the slope of the line but that doesn't give me the full equation for the line. Even if I get the full equation, I am not sure using this equation, how would I find out a point that is `x` distance away from A.

Any suggestions on how to approach this?

Answer: 
You can use the sine or the cosine (times 10) of the angle of the line to get the horizontal or vertical distance of the point that is a distance of 10 from a given point. A shortcut is to use the horizontal or vertical distance divided by the direct distance between the points to get the sine or cosine.
You can do it using vectors like this:

Let D = the difference between B and A (D = B - A)

Then any point on the line can be described by this formula:

```
point = A + Dt 

```

where t is a real number.

So just plug in any value for t to get another point. For example if you let t == 1 then the equation above reduces to point = B. If you let t = 0 then it reduces to point = A. So you can see that you can use this to find a point between A and B simply by let t range from 0 to 1. Additionally if you let t > 1, you will find a point past B.