How to Find the Distance Between a Point and a Line

To find the distance between a point and a line, you can use a straightforward formula that involves both the coordinates of the point and the equation of the line.

Suppose you have a line represented by the equation Ax + By + C = 0 and a point with coordinates (x₀, y₀). The distance d from the point to the line can be calculated using the following formula:

d = (|Ax₀ + By₀ + C|) / √(A² + B²)

Steps to Calculate the Distance:

1. Identify the coefficients A, B, and C from the line’s equation.
2. Insert the coordinates of the point (x₀, y₀) into the formula.
3. Calculate the numerator by finding the absolute value of the expression Ax₀ + By₀ + C.
4. Calculate the denominator by finding the square root of the sum of the squares of A and B.
5. Divide the result from step 3 by the result from step 4 to get the distance d.

This method provides an efficient way to measure the perpendicular distance from a point to a line, which is helpful in various applications such as geometry, physics, and engineering.