Parallel and Perpendicular Lines

Slopes

Parallel lines

m_{1} = m_{2}

and b₁ ≠ b₂

Perpendicular lines

m_{1} \cdot m_{2} = - 1 or m_{2} = - \frac{1}{m_{1}}

neither line vertical

Point to a line

d = \frac{| A x_{0} + B y_{0} + C |}{\sqrt{A^{2} + B^{2}}}

line Ax + By + C = 0, point (x₀, y₀)

Between parallel lines

d = \frac{| C_{1} - C_{2} |}{\sqrt{A^{2} + B^{2}}}

Ax + By + C₁ = 0 and Ax + By + C₂ = 0

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