Finding the distance from a point to a line

In this publication, we will consider what the distance from a point to a straight line is, and by what formula it is calculated. We will also analyze an example of solving a problem on this topic.

Calculating the distance from a point to a line

To find the distance from an arbitrary point for a line, you need to drop a perpendicular from it to this line.

Perpendicular length (d) and is the required distance.

Formula for calculating

Suppose there is a straight line given by the equation Ax + By + C = 0. The distance from it to the point L with coordinates (L_x, L_y) considered as follows:

Example of a problem

Dana straight 2x + 6y – 5 = 0. Find the distance from it to the point M (1, -3).

Decision:

Let’s use the formula above, substituting into it the data known to us according to the conditions of the problem: