Distance from Point to Line Calculator

Point to Line Distance

Find the shortest distance between a given point and a straight line. This calculator helps you solve geometry problems quickly and accurately, using the standard formula for the distance from a point to a line.

Coefficient A (for x)

Enter the coefficient of x in Ax + By + C = 0

Coefficient B (for y)

Enter the coefficient of y in Ax + By + C = 0

Constant C

Enter the constant term C in Ax + By + C = 0

Point X-coordinate (x₀)

Enter the x-coordinate of the point

Point Y-coordinate (y₀)

Enter the y-coordinate of the point

How it works

Find the shortest distance between a given point and a straight line. This calculator helps you solve geometry problems quickly and accurately, using the standard formula for the distance from a point to a line.

The Formula

The distance (D) from a point (x₀, y₀) to a line Ax + By + C = 0 is given by:
D = |Ax₀ + By₀ + C| / √(A² + B²)

Worked Example

Example: Point (3, 2) to Line 4x + 3y - 6 = 0
Let's find the distance from the point (3, 2) to the line 4x + 3y - 6 = 0. Here, x₀ = 3, y₀ = 2, A = 4, B = 3, C = -6. Substitute these values into the formula: D = |(4 * 3) + (3 * 2) + (-6)| / √(4² + 3²) D = |12 + 6 - 6| / √(16 + 9) D = |12| / √25 D = 12 / 5 D = 2.4 The distance is 2.4 units.

Tips, Assumptions & Limitations

Ensure your line equation is in the standard form Ax + By + C = 0 before entering coefficients.
The order of A, B, and C matters; make sure they correspond to x, y, and the constant term respectively.
This formula calculates the perpendicular distance, which is the shortest possible distance.

FAQ

The distance from a point to a line is the shortest possible distance between that point and any point on the line. This shortest distance is always along a line segment that is perpendicular to the given line.

The absolute value ensures that the distance is always a non-negative number, as distance is a scalar quantity and cannot be negative. The term (Ax₀ + By₀ + C) can be positive or negative depending on which side of the line the point (x₀, y₀) lies.

Yes, but you'll need to convert your line equation first. For example, if you have y = mx + b, rewrite it as mx - y + b = 0. Then, A = m, B = -1, and C = b. If you have a vertical line x = k, rewrite it as x - k = 0, so A = 1, B = 0, C = -k.