Parallel, Perpendicular and Collinear Lines

Parallel lines m_1=m_2 Distinct non-vertical lines are parallel when their gradients are equal. Two vertical lines are also parallel. Perpendicular lines m_1m_2=-1 m_2=- 1m_1 This formula requires both gradients to exist. A horizontal line is perpendicular to a vertical line. Parallel: m_1=m_2 — the lines make equal angles with the x-axis and never meet. Perpendicular: m_1m_2=-1 — the lines cross at right angles. **Gradient of l_1** | **Gradient of the perpendicular line** | **Check** 34 | - 43 | 34 x (- 43)=-1 - 25 | 52 | - 25 x 52=-1 6 | - 16 | 6 x (- 16)=-1 Collinear points Distinct points A,B,C are collinear when m_AB=m_BC, or when all three have the same x-coordinate.