Straight Lines

AB = √((x2 - x1)^2 + (y2 - y1)^2)

R = ((m x2 + n x1)/(m + n), (m y2 + n y1)/(m + n))

Midpoint = ((x1 + x2)/2, (y1 + y2)/2)

Centroid = ((x1 + x2 + x3)/3, (y1 + y2 + y3)/3)

Incentre = ((a x1 + b x2 + c x3)/(a + b + c), (a y1 + b y2 + c y3)/(a + b + c))

x' = x - h, y' = y - k

ax + by + c = 0

m = tan θ

m = (y2 - y1)/(x2 - x1)

tan θ = |(m1 - m2)/(1 + m1m2)|

tan θ' = -|(m1 - m2)/(1 + m1m2)|

Two non-vertical lines are parallel iff m1 = m2

Two non-vertical lines are perpendicular iff m1m2 = -1

Slope of AB = slope of BC