# Function Definitions

## Rectangular Coordinates

#### Pythagorean Theorem

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

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

#### Distance Formula

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

Simplified as

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

Simplified even more as this

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

#### Line Midpoint Formula

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