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In this small article we are going to look at the connection between two gradients which are perpendicular to each other.

Remember that the gradient is defined as $\frac{rise}{run}$ or $\frac{\delta y}{\delta x}$

Consider the graph below

The original gradient $=\frac{\delta y}{\delta x}$

The rotated gradient can be seen to be $=\frac{-\delta x}{\delta y}$

$\therefore$ The gradient of the perpendicular = the negative reciprocal of the other line.

Notice also that $\frac{\delta y}{\delta x}\times \frac{-\delta x}{\delta y} = -1$

Some examples

 Line Perpendicular 2 $-\frac{1}{2}$ -3 $\frac{1}{3}$ $\frac{3}{5}$ $-\frac{5}{3}$