# Distance between two parallel lines formula

Learn the formula which is used for finding distance between two parallel lines. We can say that this is the important formula that we will study in 11th coordinate geometry. Derivation of this formula no need, so just learn the formula.

We know that we have a formula for finding distance between two points in coordinate geometry. Similarly there is a formula for distance between two parallel lines also. Now let us know that formula.

## Use the below formula for finding distance between two parallel lines:

Let us consider general form of two parallel lines. Let the two parallel lines be ${ a }_{ 1 }$x + ${ b }_{ 1 }$y + ${ c }_{ 1 }$ = 0 and ${ a }_{ 1 }$x + ${ b }_{ 1 }$y + ${ c }_{ 2 }$ = 0. We know that parallel lines differ only a constant. Therefore distance between these two lines is given by

Example:

If 4x + 3y + 30 = 0 and 4x + 3y + 10 = 0 be two parallel lines then find distance between them.

Solution:

Given parallel lines are

4x + 3y + 30 = 0

4x + 3y + 10 = 0

Therefore by substituting in formula we get

= $\frac { 20 }{ 5 }$

= 4

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