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I am trying to find the coordinate of a point a fixed distance from a line segment's midpoint.I am using excel to calculate a series of problems like this. The biggest problem is that the midpoint and the point of interest are on an angle and will usually never share the same x or y coordinate.

An example of formulas used to solve this would be appreciated.

enter image description here

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    updated title, please look at image in link for clarification. – 2017-02-27
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    There is no unique point that satisfies the condition. If you know the slope of the line segment, you should be able to determine the equation of the line perpendicular to the segment and passing through its midpoint. Determining the two points that lie the required distance from the midpoint should then be straightforward. If you are not looking for points on the perpendicular, then the points you seek lie on a circle centered at the midpoint. – 2017-02-27
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    Can you give me a formula to find P from the image provided? – 2017-02-27
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    Rotate the line segment 90° about its midpoint. – 2017-02-27
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    Can you give an example of a formula? – 2017-02-27

2 Answers 2

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The midpoint of the line is of course

$$(x_m,y_m) = \left ( \frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right) $$

The vector from point $1$ to the midpoint is $ ( x_m-x_1, y_m-y_1)$ and two vectors at right angles to that are $(y_m-y_1, x_1-x_m)$ and $(y_1-y_m, x_m-x_1)$, going in opposite directions.

So if you know how to find the length of a vector - Pythagoras will help - you can scale one of those perpendicular vectors to the length you need and add to the midpoint location.

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This might be a bit late for the original question.

This definitely is the exact answer for this question.

At the time of this post I don't know how it works (once I figure out what its doing I'll edit this post), please go to the link check it out

How do you find a point at a given perpendicular distance from a line?