id: 06617820
dt: j
an: 2016e.00738
au: Choate, Jon
ti: Angle bisectors: an algebraic approach.
so: Consortium 110, 1-2 (2016).
py: 2016
pu: COMAP (Consortium for Mathematics and Its Applications), Bedford, MA
la: EN
cc: G70
ut: analytic geometry; equations of straight lines; linear equations; normal
form; angle bisectors; vectors; triangle incenter; coordinates;
parametric equations; rhombus; 2-space; 3-space; equations of planes;
tetrahedral; bisecting planes; in-spheres; cross products
ci:
li:
ab: From the text: In algebra courses students are often taught several
different forms for linear equations, the slope-intercept form
$y=mx+b$, the point-slope form $y-y_1=m(x-x_1)$, 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 pre-calculus course to find the equations of angle bisectors and
planes that bisect dihedral angles.
rv: