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Perpendicular Gradients

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

Gradient change after 90 degree rotation

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}
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