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
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.
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!