Question

@satellite73 find the equation of the line perpendicular to the line 2x+5y=12 and through the midpoint AB where A(-3,-4) and B (7,-8)

Answer 1

fist you need the slope of \(2x+5y=12\)
the slope of \(ax+by=c\) is \(-\frac{a}{b}\) so in your case the slope is \(-\frac{2}{5}\)

Answer 2

slope of perpendicular line is the negative reciprocal, in your case
\[m=\frac{5}{2}\]

Answer 3

now we need the midpoint of \((-3,-4) (7,-8)\)
take the average in each coordinate and get
\[(\frac{7-3}{2},\frac{-4-8}{2})\] or
\[(2,-6)\]

Answer 4

@satellite73 since you won't accept messages from me: how did you apply the formatting in the first message in this thread?

Answer 5

then point slope forumula
\[y=y_1=m(x-x_1)\] with
\[m=\frac{5}{2},x_1=2,y_1=-6\] and write
\[y+6=\frac{5}{2}(x-2)\] solve for \(y\) if you like or whatever form you need

Answer 6

@whpalmer4 latex
see latex practice group for examples

Answer 7

or right click on equation, select "show math as" then "latex"

Answer 8

where did the 5/2 come from?

Answer 9

the line \( 2x+5y=12\) has slope \(-\frac{2}{5}\)
perpendicular line has slope \(\frac{5}{2}\)
the "negative reciprocal"

Answer 10

Ah, the \ ( vs. \ [ was the trick, got it, thanks!

If the slope of the first line is a fraction, invert it and change the sign.

Answer 11

yeah in line latex use \( instead of \[
works in documents too

Answer 12

that is, you can use \( instead of $

Answer 13

Too bad they don't support the even shorter $eqn$

Answer 14

But they do support `$$ $$`.

$$\text{Hi.}$$

Answer 15

if i remember correctly (and i could easily be wrong) $ is a hack

Answer 16

No, $ is perfect.

Answer 17

And original.

Answer 18

like i said, i could easily be wrong

Answer 19

Yep, $ is a long-time component of the math environment. I haven't written any TeX or LaTeX documents since the days when Knuth was still occasionally working on TeX, MetaFont, Tangle, etc. Thanks for the info!

Answer 20

damn you must be as old as i am !

Answer 21

im not seeing it.

Answer 22

What aren't you seeing? You understand how to find the slope of the original line, right?

Two perpendicular lines will have a product of their slopes = -1. Think of the graphs of \(y=x\) and \(y = -x\) — they make a nice big symmetrical X over the origin, and are perpendicular. The slope of \(y=x\) is 1, and the slope of \(y = -x\) is -1, because they are in slope-intercept form:$$y=mx+b$$where m is slope and b is y-intercept.

Now, if you have two numbers \(a,b\) where \(a*b = -1\), you can find b from a by \[b = -\frac{1}{a}\]

Dividing by a fraction is the same as multiplying by the reciprocal of the fraction, so \[-\frac{1}{-\frac{2}{5}} = -1 * -\frac{5}{2} = \frac{5}{2}\]