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 1

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.