What is the slope of any line perpendicular to the line passing through (4,2) and (-1,10)?

1 Answer
Oct 20, 2017

5/8

Explanation:

First figure out the slope of the line that passes through those points using the slope formula:

(y_2-y_1)/(x_2-x_1) where y_2=10, y_1=2 and x_2=-1, x_1=4

So:

(10-2)/(-1-4)=8/-5=slope

NOTE: You could also let y_2=2, y_1-10 and x_2=4, x_1=-1
Which leads to the same answer (thanks Tony B.!):

(2-10)/(4-(-1))=(-8)/5=slope

Perpendicular lines always have different signed slopes (meaning if one line's slope is positive, the perpendicular line's slope is negative and similarly negative -> positive). Thus our slope is positive.

Also perpendicular lines are reciprocals of each other so our new slope is:

5/8