Parallel lines $m_1=m_2$ Distinct non-vertical lines are parallel when their gradients are equal.

Question

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 $m_1m_2=-1\qquad m_2=-\dfrac1{m_1}$ 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 lineCheck $\dfrac{3}{4}$ $-\dfrac{2}{5}$ $6$ Collinear points Distinct points $A,B,C$ are collinear when $m_{AB}=m_{BC}$, or when all three have the same $x$-coordinate.

Accepted Answer

$\text{Collinear: }m_{AB}=m_{BC}=m_{AC}\qquad \text{Parallel: }m_{PQ}=m_{RS}$

Gradient of \(l_1\)	Gradient of the perpendicular line	Check
\(\dfrac{3}{4}\)
\(-\dfrac{2}{5}\)
\(6\)

Parallel, Perpendicular and Collinear Lines

Parallel, Perpendicular and Collinear Lines

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