Function Definitions

Rectangular Coordinates

Pythagorean Theorem

This defines a right triangle and can be used to determine if the coordinates define a right triangle.

$a^{2}+b^{2}=c^{2}$

Distance Formula

$d^{2}={|x_{2}-x_{1}|}^{2}+{|y_{2}-y_{1}|}^{2}$

Simplified as

$d={\sqrt {{|x_{2}-x_{1}|}^{2}+{|y_{2}-y_{1}|}^{2}}}$

Simplified even more as this

$d={\sqrt {(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}}$

Line Midpoint Formula

$Midpoint=\left({\frac {x_{1}+x_{2}}{2}},{\frac {y_{1}+y_{2}}{2}}\right)$