# Expression for Distance between two lines

• Apr 27th 2012, 12:42 PM
user654321
Expression for Distance between two lines
Find the equation of the line perpendicular to the line ax + by = d which passes through the origin.
Hence derive a formula for the distance of the line ax + by = d from the origin.

Hence find an expression for the distance between two parallel lines.

Anyone give me any help with this please?

Cheers

Chloe :)
• Apr 27th 2012, 01:49 PM
Plato
Re: Expression for Distance between two lines
Quote:

Originally Posted by user654321
Find the equation of the line perpendicular to the line ax + by = d which passes through the origin. Hence derive a formula for the distance of the line ax + by = d from the origin.
Hence find an expression for the distance between two parallel lines.

$\displaystyle bx-ay=0$ is the equation of the line perpendicular to the line $\displaystyle ax + by = d$ which passes through the origin.
• Apr 27th 2012, 02:17 PM
MathoMan
Re: Expression for Distance between two lines
Simple version:
If you have two parallel lines and you want to calculate the distance between them then simply choose any point on one of the given lines and calculate the distance between that point and the other line. Easy as $\displaystyle \pi$.

Version that was given to you: calculate the distance of each line to the origin. Say distance of the first line to the origin is $\displaystyle d_1$ and distance of the second line to the origin is $\displaystyle d_2$. Distance between the lines can be calculated as $\displaystyle |d_1 - d_2|$.