Distance, Midpoint and Slope

Two points

Distance

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

Midpoint

M = (\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})

Slope

m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}

x₂ ≠ x₁

Point dividing in the ratio m : n

P = (\frac{m x_{2} + n x_{1}}{m + n}, \frac{m y_{2} + n y_{1}}{m + n})

Point a fraction k of the way

P = (x_{1} + k (x_{2} - x_{1}), y_{1} + k (y_{2} - y_{1}))

k = m/(m + n)

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