Line l has a slope of 98. The line through which of the following pair of points is perpendicular to l? A. (−9,−6),(3,3) B. (9,−2),(−6,6) C. (−5,−6),(3,3) D. (3,−5),(−6,3)
We can employ some logic to reduce the answers we need to test. We know that the slope perpendicular to line l has to have a negative reciprocal slope, so a slope of[tex] -\frac{9}{8} [/tex]. We see that in A and C, as x increases so does y. That means the slope of these equations are positive, which we don't want. Now for some algebra:
[tex] m=\frac{y_2-y_1}{x_2-x_1} \implies\\ B. \frac{6+2}{-6-9}=\frac{8}{-15} \\ D. \frac{3+5}{-6-3}=-\frac{8}{9} [/tex]
We se that D has the correct slope so that must be the answer.
