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

Find the distance to the origin of the line r ≡ 3x − 4y − 25 = 0. 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?   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?   ### 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.  The best Maths tutors available
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1st lesson free!  4.9 (26 reviews)
Intasar
£36
/h
1st lesson free!  5 (17 reviews)
Matthew
£25
/h
1st lesson free!  4.9 (13 reviews)
Paolo
£25
/h
1st lesson free!  4.9 (7 reviews)
Dr. Kritaphat
£49
/h
1st lesson free!  5 (28 reviews)
Ayush
£60
/h
1st lesson free!  4.9 (9 reviews)
Petar
£27
/h
1st lesson free!  5 (14 reviews)
Farooq
£40
/h
1st lesson free!  5 (9 reviews)
Tom
£22
/h

## Example

Find the distance between the lines: r ≡ 3 x − 4 y + 4 = 0 and s ≡ 9 x − 12 y − 4 = 0.    The distance between two parallel lines also can be expressed as follows: ## Example

Calculate the distance between the following lines:  Need a Maths teacher?

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Emma

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places.