Question

Is the line through points P(0, –9) and Q(2, –8) perpendicular to the line through points R(1, 4) and S(3, 3)? Explain

Answer 1

If the gradient of one line is $m$, then any line that's perpendicular to it must have a gradient $\frac{-1}{m}$. Calculate the gradients of both lines, and see if they are related like this!

Answer 2

The quickest way to tell if a line is perpendicular is to find the slope, so you'll need to get the slope for both lines

PQ = ((-8) - (-9))/(2 - 0) = 1/2

and, for reference, a perpendicular slope is the negative reciprocal of the original (so we're looking for -2)

RS = (3 - 4)/(3 - 1) = -1/2

so, no, these two lines aren't perpendicular because the slope of RS is only the negative of PQ, not the negative reciprocal.