Proof (Two Dimensions)
Consider the line given by and a point . For ease, consider a point given by, where (since is on the line). Then we have
- .
Here is simply the angle between the line and the -axis, such that
- .
Using the Pythagorean theorem we have, and
- .
This can be extended to the case where is any point on the line, however, one can always choose such that one coordinate is common to to simplify the formulation.
Read more about this topic: Perpendicular Distance
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