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

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    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 Rē. 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.
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    Quote Originally Posted by Ulysses View Post
    Hi there. I'm tryin to find a point, lets call it C. I'm working on a Rē. 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.

    Finding a point on a line, given another point on the same line, and knowing its dist-circleline.png

    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).
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    Thanks undefined!
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