What is the slope of any line perpendicular to the line passing through $(14,19)$ and $(12,15)$ ?

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Answer 1 · 2015-12-30T02:00:46

$-1/2$

Let the slope of this line be $m$ and that of the line perpendicular to it be $m'$ , then $m.m' = - 1$

$=>m'= - 1/m = - 1/((y_2 - y_1)/(x_2 - x_1))=-(x_2-x_1)/(y_2-y_1)=- (12-14)/(15-19)=-(-2)/-4=-2/4$
$implies m'=-2/4=-1/2$ .

$implies$ the slope of line perpendicular to the line passing through the given points is $-1/2$ .

What is the slope of any line perpendicular to the line passing through (14,19)(14,19) and (12,15)(12,15)?