Slopes of perpendicular lines..

**zoso** · July 18th 2006, 08:52 PM

if

a and 3
-
2

are the slopes of perpendicular lines, a =

someone wanna explain negative recipricals to me?

**malaygoel** · July 18th 2006, 09:05 PM

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

**NineZeroFive** · July 19th 2006, 02:11 AM

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 $3/2$ would be $m=-2/3$

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

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

Remember, parallel lines have the same slope.

Hope this helps..
-NineZeroFive

**Quick** · July 19th 2006, 05:02 AM

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 $3/2$ would be $m=-2/3$

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

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

Remember, parallel lines have the same slope.

Hope this helps..
-NineZeroFive

the question was if a line with the slope $\frac{a}{2}$ is perpendicular to a line with the slope $3$ then what is the value of a?

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

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

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

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

check:

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

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

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

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

$\neg 1=\neg 1$

Interesting use of negative reciprocal:

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

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

**malaygoel** · July 19th 2006, 06:31 PM

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

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

Family of lines perpendicular to the given line
$bx-ay+k=0$
or, $-bx+ay+k=0$ (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

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