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: 
There are always two points on each line:

* get the vector from `A` to `B` (subtract the coordinates)
* normalize the vector (divide by its length; pythagorean theorem)
* multiply the vector by 10 **or** -10
* add the vector to `A` to get `C`

Note that if `A==B`, the line is not defined, and this algorithm causes a division by zero. You may want to add a test for equality at the beginning.
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.