Difference between revisions of "Distance formula"
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Therefore the perpendicular distance from <math>(x_1,y_1)</math> to the line <math>ax+by+c = 0</math> is: | Therefore the perpendicular distance from <math>(x_1,y_1)</math> to the line <math>ax+by+c = 0</math> is: | ||
− | <cmath>|t| = \dfrac{|ax_1 + by_1 + c|}{\sqrt | + | <cmath>|t| = \dfrac{|ax_1 + by_1 + c|}{\sqrt{a^2+b^2}}</cmath> |
Revision as of 14:35, 30 July 2014
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
This article is a stub. Help us out by expanding it.
--Shortest distance from a point to a line--
the distance between the line and point
is
---Proof---
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:
, so:
Therefore the perpendicular distance from to the line
is: