Difference between revisions of "Distance formula"
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--Shortest distance from a point to a line-- | --Shortest distance from a point to a line-- | ||
the distance between the line <math>ax+by+c = 0</math> and point <math>(x_1,y_1)</math> is | the distance between the line <math>ax+by+c = 0</math> and point <math>(x_1,y_1)</math> is | ||
− | <cmath>|ax_1+by_1+c| | + | <cmath>\dfrac{\|ax_1+by_1+c\|}{\sqrt{a^2+b^2}}</cmath> |
---Proof--- | ---Proof--- |
Revision as of 14:29, 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
So the perpendicular line through
is:
where
is a 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
ax+by+c = 0 is: