
06617820
j
2016e.00738
Choate, Jon
Angle bisectors: an algebraic approach.
Consortium 110, 12 (2016).
2016
COMAP (Consortium for Mathematics and Its Applications), Bedford, MA
EN
G70
analytic geometry
equations of straight lines
linear equations
normal form
angle bisectors
vectors
triangle incenter
coordinates
parametric equations
rhombus
2space
3space
equations of planes
tetrahedral
bisecting planes
inspheres
cross products
From the text: In algebra courses students are often taught several different forms for linear equations, the slopeintercept form $y=mx+b$, the pointslope form $yy_1=m(xx_1)$, and the standard form $ax+by+c=0$. I would like to add a fourth form, the normal form $ax+by+c=0$ with $\sqrt{a^2+b^2}=1$. The rest of this article will use this form and some of the vector algebra that is taught in an upper level precalculus course to find the equations of angle bisectors and planes that bisect dihedral angles.