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 m

_{a}=m

_{b}

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 m

_{a}x m

_{b}=-1