Coordinate/Analytical Geometry

equation of a line

$$y = mx+c$$
$$y-y_{1} = m(x-x_{1})$$

Distance Formula



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


Midpoint Formula



$$M({x_{1}+x_{2}}/2;{y_{1}+y_{2}}/2)$$


Gradient



$$m = {rise}/{run}$$
$$m = {y_{2}-y_{1}}/{x_{2}-x_{1}}$$
$$m = tan(θ)$$


Parallel Lines




a and b are parallel to each other if the gradient of a is equal to the gradient of b. ie ma=mb


Perpendicular Lines




a and b are perpendicular to each other if the product of the gradients of a and b is equal to -1. ie ma x mb=-1