Question

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.)
This is a topic on a class discussion, and I honestly don't understand it. I need help mainly on the second part of writing an example rather than the first part. Please help=)

Answer 1

\[0<m_1<1\]
when lines are perpendicular, their slopes are negative reciprocals so,
\[
m_2=-{1\over m_1}\\
0<m_1<1\\
\infty>{1\over m_1}>1\\
\boxed{-\infty<m_2<-1}
\]

Answer 2

So that is one possible answer for the second half?

Answer 3

@Nurali the solution you've posted seems controvercial

Answer 4

so, a line perpendicular to AB with slope of \(m_1\), has a slope of \(m_2\).
then we follow the above steps.

Answer 5

it is given that
\(0<m_1<1\)

Answer 6

so, we flip everything.. i.e., take the reciprocal. and the inequality signs flip
\[{1\over0}>{1\over m_1}>{1\over 1}\\
\implies \infty>{1\over m_1}>1\]

Answer 7

if we multiply the inequality by -1, the signs flip again
\[-\infty<{-1\over m_1}<-1\]

Answer 8

but, by the property of perpendicular lines, their slopes are negative reciprocals of eachother.
i.e., \(m_2=\Large {-1\over m_1}\)

Answer 9

so, we finally get:
\[-\infty <m_2<-1\]

Answer 10

kapeesh?

Answer 11

I wish, I feel rather stupid right now haha. I honestly don't understand. I know this is a correct answer, it is an example my teacher posted but I don't understand how to create one myself
y = 1/2 x + 10 and y = -2 x + 15

Answer 12

its ok.
did you follow the steps I posted up here one by one?
the idea behind this is tis:
\(\mathbf{\text{if two lines with slopes m_1 and m_2 are peprendicular,}}\\
\mathbf{\text{ then m_1= -1/m_2}}\)