Difference between revisions of "Distance formula"
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The equation <math>ax + by + c = 0</math> can be written as <math>y = -(a/b)x - (c/a)</math> | The equation <math>ax + by + c = 0</math> can be written as <math>y = -(a/b)x - (c/a)</math> | ||
So the perpendicular line through <math>(x_1,y_1)</math> is: | So the perpendicular line through <math>(x_1,y_1)</math> is: | ||
− | + | <cmath>(x-x_1)/a=(y-y_1)/b=t/\sqrt(a^2+b^2)</cmath> | |
where <math>t</math> is a parameter. | where <math>t</math> is a parameter. | ||
Revision as of 20:26, 7 November 2013
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: