# Math Help - Finding a point on a line, given another point on the same line, and knowing its dist

1. ## 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: $y=\displaystyle\frac{x}{2}+\displaystyle\frac{1}{2 }$ And that the distance to the point B(1,1), that belongs to L is $\sqrt[ ]{20}$.

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

2. 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: $y=\displaystyle\frac{x}{2}+\displaystyle\frac{1}{2 }$ And that the distance to the point B(1,1), that belongs to L is $\sqrt[ ]{20}$.

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 $2 * \sqrt{5} = \sqrt{4*5} = \sqrt{20}$. 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).

3. Thanks undefined!