# Find the Distance between two parallel Lines

#### AlbertMark

how to use the equation D=c1-c2/(A)^2+(B)^2

in this given question :
4x+y=6
12x+3y=14

i know how to use it on same A and B like this
3x+12y-4=0
3x+12y+15=0

but in the another given im confused

#### Plato

MHF Helper
how to use the equation D=c1-c2/(A)^2+(B)^2
in this given question :
[4x+y=6
12x+3y=14
I will be frank: the given equation(formula) for distance is confusing.
If $P: (p,q)~\&~\ell: Ax+By+C=0$ are a point and a line, the the distance $\mathbb{D}(P,\ell)=\dfrac{|Ap+Bq+C|}{A^2+B^2}$

For parallel lines: pick a point $P$ on one find the distance to the other.

In your problem it could be $(1,2), A=12,~B=3,~\&~C=-14$

#### Archie

$$\displaystyle 4x+y=6 \iff 12x+3y-18=0$$ and $$\displaystyle 12x+3y=14 \iff 12x+3y-14=0$$ which you say you can solve.

#### bjhopper

I will be frank: the given equation(formula) for distance is confusing.
If $P: (p,q)~\&~\ell: Ax+By+C=0$ are a point and a line, the the distance $\mathbb{D}(P,\ell)=\dfrac{|Ap+Bq+C|}{A^2+B^2}$

For parallel lines: pick a point $P$ on one find the distance to the other.

In your problem it could be $(1,2), A=12,~B=3,~\&~C=-14$

Your distance formula needs to be corrected

#### Plato

MHF Helper
Your distance formula needs to be corrected
$\sqrt{A^2+B^2}$ thanks