# Thread: Slopes of perpendicular lines..

1. ## Slopes of perpendicular lines..

if

a and 3
-
2

are the slopes of perpendicular lines, a =

someone wanna explain negative recipricals to me?

2. Originally Posted by zoso
if

a and 3
-
2

are the slopes of perpendicular lines, a =

someone wanna explain negative recipricals to me?
you got it a/2 *3=-1
a=-2/3

Malay

3. Originally Posted by zoso
if

a and 3
-
2

are the slopes of perpendicular lines, a =

someone wanna explain negative recipricals to me?
What do you mean a=? Are you just using it as another variable to the slope (m)? Usually the slopes of all lines are m=, regardless of them being perpendicular. In your case, the slope of the line perpendicular to a line with the slope of$\displaystyle 3/2$ would be $\displaystyle m=-2/3$

Negative reciprocals are basically just the opposite of the original fraction/whole number (just flip it).

Examples:
$\displaystyle m=3/1$, the negative reciprocal is: $\displaystyle -1/3$
$\displaystyle m=5/2$, the negative reciprocal is: $\displaystyle -2/5$
$\displaystyle m=-1/5$, the negative reciprocal is: $\displaystyle 5$
$\displaystyle m=-4/5$, the negative reciprocal is: $\displaystyle 5/4$

Remember, parallel lines have the same slope.

Hope this helps..
-NineZeroFive

4. Originally Posted by 905
What do you mean a=? Are you just using it as another variable to the slope (m)? Usually the slopes of all lines are m=, regardless of them being perpendicular. In your case, the slope of the line perpendicular to a line with the slope of$\displaystyle 3/2$ would be $\displaystyle m=-2/3$

Negative reciprocals are basically just the opposite of the original fraction/whole number (just flip it).

Examples:
$\displaystyle m=3/1$, the negative reciprocal is: $\displaystyle -1/3$
$\displaystyle m=5/2$, the negative reciprocal is: $\displaystyle -2/5$
$\displaystyle m=-1/5$, the negative reciprocal is: $\displaystyle 5$
$\displaystyle m=-4/5$, the negative reciprocal is: $\displaystyle 5/4$

Remember, parallel lines have the same slope.

Hope this helps..
-NineZeroFive
the question was if a line with the slope $\displaystyle \frac{a}{2}$ is perpendicular to a line with the slope $\displaystyle 3$ then what is the value of a?

which (this is just extending what Malay said) would mean that $\displaystyle 3$ and $\displaystyle \frac{a}{2}$ are negative reciprocal, which implies that multiplied together they equal -1, now solve for a...

$\displaystyle \frac{a}{2}\times 3=\neg 1$

$\displaystyle \frac{a}{2}=\frac{\neg 1}{3}$

$\displaystyle \boxed{a=\frac{\neg 2}{3}}$

check:

$\displaystyle \frac{a}{2}\times 3=\neg 1$

$\displaystyle \frac{\frac{\neg 2}{3}}{2}\times 3=\neg 1$

$\displaystyle \frac{\neg 2}{6}\times 3=\neg 1$

$\displaystyle \frac{\neg 6}{6}=\neg 1$

$\displaystyle \neg 1=\neg 1$

Interesting use of negative reciprocal:

Just a bit of info you might like nzf, in a linear equation like $\displaystyle y=mx+b$ to find the x-intercept you multiply the y-intercept by the slopes negative reciprocal.

~ $\displaystyle Q\!u\!i\!c\!k$

5. Slope are used to find family of lines.
You are given a line $\displaystyle ax+by+c=0$

Family of lines parallel to the given line
$\displaystyle ax+by+k=0$(Same coefficients of x and t means same slope, k is a parameter)

Family of lines perpendicular to the given line
$\displaystyle bx-ay+k=0$
or,$\displaystyle -bx+ay+k=0$(Swapping the cofficients of x and y and multiplying anyone of then by -1 gives a perpendicular line, this is due to negative reciprocal)

Keep Smiling
Malay