Point to Line Distance Calculator

Formula

The formula to calculate the Point to Line Distance is:

\[ PLD = \frac{|a \cdot x1 + b \cdot y1 + c|}{\sqrt{a^2 + b^2}} \]

Where:

\(PLD\) is the Point to Line Distance
\(x1, y1\) are the coordinates of the point \((x1, y1)\)
\(a, b, c\) are the coefficients of the line equation \(ax + by + c = 0\)

What is Point to Line Distance?

The Point to Line Distance refers to the shortest distance between a given point and a line. This distance is calculated using the formula involving the coordinates of the point and the coefficients of the line equation. It is a crucial concept in geometry and is used in various applications, including computer graphics, engineering, and physics.

Example Calculation

Let's assume the following values:

Point Coordinates: \(x1 = 3\), \(y1 = 4\)
Line Equation Coefficients: \(a = 1\), \(b = -2\), \(c = 1\)

Using the formula:

\[ PLD = \frac{|1 \cdot 3 + (-2) \cdot 4 + 1|}{\sqrt{1^2 + (-2)^2}} = \frac{|3 - 8 + 1|}{\sqrt{1 + 4}} = \frac{| -4 |}{\sqrt{5}} = \frac{4}{\sqrt{5}} \approx 1.79 \]

The Point to Line Distance (PLD) is approximately 1.79.