angle bisector as locus

If  0<α<180o,  then the angle bisectorMathworldPlanetmath of α is the locus of all such points which are equidistant from both sides of the angle (it is proved by using the AAS and SSA theorems).

The equation of the angle bisectors of all four angles formed by two intersecting lines

a1x+b1y+c1= 0,a2x+b2y+c2= 0 (1)


a1x+b1y+c1a12+b12=±a2x+b2y+c2a22+b22, (2)

which may be written in the form

xsinα1-ycosα1+h1=±(xsinα2-ycosα2+h2) (3)

after performing the divisions in (2) termwise; the angles α1 and α2 then the slope angles of the lines.

Note.  The two lines in (2) are perpendicularMathworldPlanetmathPlanetmathPlanetmath, since their slopes sinα1±sinα2cosα1±cosα2 are opposite inversesPlanetmathPlanetmath of each other.

Title angle bisector as locus
Canonical name AngleBisectorAsLocus
Date of creation 2013-03-22 17:10:41
Last modified on 2013-03-22 17:10:41
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 11
Author pahio (2872)
Entry type Definition
Classification msc 51N20
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