Perpendicular Lines

Perpendicular lines are two lines which meet at 90°.

If a line has the gradient of $m$ , a line perpendicular will have the gradient of $-\frac{1}{m}$ . If two lines are perpendicular, the product of their gradients will be $-1$ .

Example: Calculating a perpendicular gradient with a variable

m_{1} = 5 a m_{2} = - \frac{1}{5 a}

Example: Identifying if two lines are perpendicular

3 x - y - 2 = 0 x + 3 y - 6 = 0 3 \times - \frac{1}{3} = - 1 y = 3 x - 2 m = 3 - x = 3 y - 6 - x - 6 = 3 y 3 y = - x - 6 y = - \frac{1}{3} x - 2 m = - \frac{1}{3}

Example question from book: $3x - y - 2 = 0$ and $x + 3y - 6 = 0$