help on analytic geometry

• Dec 1st 2006, 08:22 AM
help on analytic geometry
Help!!! Just this 1 problem

find the equations of two lines through A, one parallel and the other perpendicular to the line defined by the given equation:
30.) \$\displaystyle A(-4,0), 4x+3y = 2 \$
thats all for today

thank you very much for all your helps!
• Dec 1st 2006, 09:42 AM
CaptainBlack
Quote:

Help!!! Just this 1 problem

find the equations of two lines through A, one parallel and the other perpendicular to the line defined by the given equation:
30.) \$\displaystyle A(-4,0), 4x+3y = 2 \$
thats all for today

thank you very much for all your helps!

Rewrite \$\displaystyle 4x+3y = 2 \$ in standard form: \$\displaystyle y=-(4/3)x+2/3\$ so the slope of lines parallel to this all have slope \$\displaystyle -4/3\$, and the slope of a line perpendicular to this has slope \$\displaystyle 3/4\$.

Now the equation of the parallel line is:

\$\displaystyle
y=-(4/3)x+c
\$

now it goes through \$\displaystyle (-4,0)\$, so \$\displaystyle 0=-(4/3)(-4)+c\$
so \$\displaystyle c=-16/3\$, so:

\$\displaystyle
y=-(4/3)x-16/3
\$.

A similar procedure gives the line at right angle to this one as:

\$\displaystyle
y=(3/4)x+3
\$

RonL