Anayltic geometry

mj.alawami · #1 $Old$ June 26th, 2009, 12:15 PM

Question:
Find the distance between the given pairs?
$4x+3y+8=0$ , $4x+3y-0=0$

Attempt:

I did the distance formula with origin (0,0) and got:
$d1=\frac{8}{5} ,d2=\frac{0}{5}$
So,since they are of the same sign
$|\frac{8}{5} - \frac{0}{5} =\frac{8}{5}|$

Am I correct?
Thank you.

Plato · #2 $Old$ June 26th, 2009, 12:33 PM

You have found the correct anawer.

Here is an easy to remember formula: $\begin{gathered} P = (p,q)\;\& \,\ell :Ax + By + C = 0 \hfill \\ d(P;\ell ) = \frac{{\left| {Ap + Bq + C} \right|}} {{\sqrt {A^2 + B^2 } }} \hfill \\ \end{gathered}$

I would choose a easy to use point on the second line say $(3,-4)$ and use the formula to find the distance to the other line.