The distance formula is a direct application of the Pythagorean Theorem in the setting of a Cartesian coordinate system. In the two-dimensional case, it says that the distance between two points and is given by . In the -dimensional case, the distance between and is .
Shortest distance from a point to a line
the distance between the line and point is
The equation can be written as Thus, the perpendicular line through is: where is the parameter.
will be the distance from the point along the perpendicular line to . So and
This meets the given line , where:
Therefore the perpendicular distance from to the line is:
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