Distance from a Point to a Line

The distance from a point to a straight line is the length of a line segment drawn from the point that forms a perpendicular angle with the straight line.

Distance from a Point to a Line

Distance from a Point to a Line

Distance from a Point to a Line Formula

Find the distance from Point P = (2, −1) to the line r ≡ 3 x + 4 y = 0.

Distance from a Point to a Line Example


Distance to the Origin

Distance to the Origin Formula

Ejemplos

Find the distance to the origin of the line r ≡ 3x − 4y − 25 = 0.

Distance to the Origin Calculations


A straight line is parallel to another which has an equation of r ≡ 5x + 8y − 12 = 0, and is 6 units from the origin. What is the equation of this line?

Distance to the Origin Example

Distance to the Origin Calculations

Distance to the Origin Solution


A straight line is perpendicular to another that has an equation of r ≡ 5x − 7y + 12 = 0 and is 4 units away from the origin. What is the equation of this line?

Perpendicular Lines

Distance to the Origin Calculations

Line Distance Solution


Distance between Parallel Lines

Distance between Parallel Lines

To find the distance between two parallel lines, take any point P from one of the lines and calculate the direct distance to the other.

Distance between Parallel Lines

 

Example

Find the distance between the lines: r ≡ 3 x − 4 y + 4 = 0 and s ≡ 9 x − 12 y − 4 = 0.

Distance between Parallel Lines Example

Distance between Parallel Lines Calculations

Distance between Parallel Lines Calculations

Distance between Parallel Lines Solution


The distance between two parallel lines also can be expressed as follows:

Distance between Parallel Lines Formula

Example

Calculate the distance between the following lines:

Distance between Parallel Lines Example

Distance between Parallel Lines Solution