## Distance of a point from a line

Here what we want is the shortest distance of a point from a line. This is the perpendicular distance of the point to the line

Steps

- Find the gradient of the line
- Find the gradient of the perpendicular to the line (the negative reciprocal)
- Find the equation of the line that goes through the point and has the perpendicular gradient
- Find the point of intersection between the original line and the line we have just found
- Find the distance between the original point and the point just found

## Example

Find the shortest distance between the point

The gradient of the line is 2

The gradient perpendicular to the line is

Using

So

To find point of intersection let

So

Distance between the two points is

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Categories: Geometry

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