Question

What is the slope of any line perpendicular to the line passing through `(-21,2)` and `(-32,5)`?

Answer 1

slope of the perpendicular line `=11/3`

Explanation:

First we need to find the slope of the line passing through the points: `(-21, 2) and (-32, 5)`, the slope `m` between the points:
`(x_1, y_1) and (x_2, y_2)` is given by:
`m=(y_2-y_1)/(x_2-x_1)`, so in this case:
`m=(5-2)/(-32-(-21))`, simplifying we get:
`m=3/(-32+21)=3/-11=-3/11`
Now the perpendicular lines have slopes that are negative reciprocals, so if `m_1 and m_2` are the slopes of the two perpendicular lines then:
`m_2=-1/m_1`, therefore in this case:
`m_2= -1/(-3/11) = 11/3`