Straight Lines — Formula Sheet

PQ = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

\left( \frac{mx_2 + nx_1}{m + n}, \frac{my_2 + ny_1}{m + n} \right)

\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)

\frac{1}{2} \left| x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \right|

m = \tan \theta

m = \frac{y_2 - y_1}{x_2 - x_1}

tan θ = \left| \frac{m_2 - m_1}{1 + m_1 m_2} \right|

y - y_0 = m(x - x_0)

y - y_1 = \frac{y_2 - y_1}{x_2 - x_1}(x - x_1)

y = mx + c

y = m(x - d)

\frac{x}{a} + \frac{y}{b} = 1

The general linear equation is Ax + By + C = 0, where A and B are not zero simultaneously.

If 1 + m1m2 = 0, the lines are perpendicular.