Please help///;

Question

Please help///;

anonymous · Answer

Suppose the slope of line AB is greater than 0 and less than 1. What inequality represents the slope of a line perpendicular to line AB? (Hint: This part of the question has one right answer.) Give an example of the slopes for a pair of lines that would satisfy both inequalities. (Many examples are possible.)

agent0smith · Answer

For perpendicular lines, with slope m1 and m2, $$m _{2} = -\frac{ 1 }{ m _{1} }$$

agent0smith · Answer

1 divided by a number less than 1, is always greater than 1. Thus, -1 divided by a number less than 1, is always less than -1.

anonymous · Answer

0<AB<1 then the perpendicular would be -infinity<line<-1
I think

agent0smith · Answer

eg 1/0.25 = 4
and -1/0,25 = -4

so $$m _{2} < -1 $$

agent0smith · Answer

No.. to the person who... asked the question :P

Give an example of the slopes for a pair of lines that would satisfy both inequalities.

Pick any number between 0 and 1 for slope m1. Then find m2 from the formula above.

anonymous · Answer

im so confused...

anonymous · Answer

pick a number between 0 & 1
say, 0.5

anonymous · Answer

okay..

anonymous · Answer

If that is the slope of AB
we'll label that $$m_1=0.5$$

anonymous · Answer

alright.

anonymous · Answer

now, the formula:
$$m_2=-\frac{ 1 }{ m_1 }$$

anonymous · Answer

so, -1/0.5 is -2

anonymous · Answer

right,

anonymous · Answer

so if you keep doing that, you'll notice a pattern

anonymous · Answer

that the slope of the line perpendicular is always going to be more than negative infinity but less than -1

anonymous · Answer

you can try with a really small number like:
0.0000001
and the perpendicular line would be:
-10000000

anonymous · Answer

the line will always be:
$$-\infty<x<-1$$
x being the slope of the line

agent0smith · Answer

@Chelsea04 I don't think you need to add the neg. infinity. x < -1 is the same thing.

anonymous · Answer

RIGHT YOU ARE!!! WHOOPS!!! MY BAD!!!

anonymous · Answer

I'm thinking of other stuff, like writing it in the interval thing @agent0smith
xϵ(−∞,−1]

agent0smith · Answer

No worries :) it's not like it's incorrect anyway, it's just kinda implied that x is greater than neg. infinity, so no need to write it there.

anonymous · Answer

Yea, I'm aware :) thank-you for that :)