Editing Triangle (section)

== Location of a point ==
One way to identify locations of points in (or outside) a triangle is to place the triangle in an arbitrary location and orientation in the [[Cartesian plane]], and to use Cartesian coordinates. While convenient for many purposes, this approach has the disadvantage of all points' coordinate values being dependent on the arbitrary placement in the plane.{{sfn|Oldknow|1995}}

Two systems avoid that feature, so that the coordinates of a point are not affected by moving the triangle, rotating it, or reflecting it as in a mirror, any of which gives a congruent triangle, or even by rescaling it to a similar triangle:<ref>{{multiref
|{{harvnb|Oldknow|1995}}
|{{harvnb|Ericson|2005|p=[https://books.google.com/books?id=WGpL6Sk9qNAC&pg=PA46 46&ndash;47]}}
}}</ref>
* [[Trilinear coordinates]] specify the relative distances of a point from the sides, so that coordinates <math>x : y : z</math> indicate that the ratio of the distance of the point from the first side to its distance from the second side is <math>x : y </math>, etc.
* [[Barycentric coordinates (mathematics)|Barycentric coordinates]] of the form <math>\alpha :\beta :\gamma</math> specify the point's location by the relative weights that would have to be put on the three vertices in order to balance the otherwise weightless triangle on the given point.