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
2 answers:
If the gradient of one line is
, then any line that's perpendicular to it must have a gradient
. Calculate the gradients of both lines, and see if they are related like this!
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 <em>reciprocal</em>.
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