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 :)

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.

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 $\displaystyle |d_1 - d_2|$.