Video Transcript
If line 𝐴𝐵 is perpendicular
to line 𝐶𝐷 and the slope of line 𝐴𝐵 equals two-fifths, find the slope of
line 𝐶𝐷.
Here, we are told that we have
two perpendicular lines 𝐴𝐵 and 𝐶𝐷. Knowing that two lines are
perpendicular means that we know something about the relationship between their
slopes. If we define line 𝐴𝐵 to have
a slope of 𝑚 sub one and line 𝐶𝐷 to have a slope of 𝑚 sub two, then we know
that 𝑚 sub two is equal to negative one over 𝑚 sub one. Given that the slope 𝑚 sub one
of line 𝐴𝐵 is two-fifths, then 𝑚 sub two is equal to negative one over
two-fifths. This simplifies to negative
five over two. Because these two lines are
perpendicular, their slopes will be the negative reciprocal of one another. And so the slope of line 𝐶𝐷
is negative five over two.
