Thread: Finding a point on a line, given another point on the same line, and knowing its dist

Hi there. I'm tryin to find a point, lets call it C. I'm working on a R². What I know is that the point belongs to the line L: And that the distance to the point B(1,1), that belongs to L is .

How can I find it? I know there are two points, cause of the distance over the line.

Originally Posted by Ulysses

Hi there. I'm tryin to find a point, lets call it C. I'm working on a R². What I know is that the point belongs to the line L: And that the distance to the point B(1,1), that belongs to L is .

How can I find it? I know there are two points, cause of the distance over the line.

Hi Ulysses,

A straightforward way to solve is to consider the slope of the line, 1/2, which means that for a rise of 1, we have a run of 2.



The hypotenuse length was obtained using the Pythagorean theorem. Then notice that . That means that for a run of 4 (or -4) and rise of 2 (or -2) starting from B we get to C.

So C = (5, 3) or C = (-3, -1).

Thanks undefined!