Gradients — Comparing Gradients of Two Lines

Find the gradient of a line segment, the midpoint of the line interval and the distance between 2 distinct points on the Cartesian plane.

Things you should know.

Method

Worked example

1. Calculate gradients $(m)$ of both lines$m_{1} = \tfrac{2}{3} \text{ and } m_{2} = -\tfrac{3}{2}$

2. If $m_{1} = m_{2}$, the lines are PARALLEL$m_{1} \neq m_{2} \therefore \text{ not parallel}$
3. If the gradients are different, multiply together$m_{1} \times m_{2} = \tfrac{2}{3} \times \tfrac{-3}{2} = -1$
4. If $m_{1} \times m_{2} = -1$, the lines are PERPENDICULAR$\therefore \text{ perpendicular}$

Practice

Determine the gradients between the following points, and state which lines are parallel to each other and which are perpendicular: $A(1;3)$, $B(6;9)$, $C(9;6)$, $D(4;0)$, $E(5;4.5)$