What is the slope of any line perpendicular to the line passing through $(2,2)$ and $(3,-5)$ ?

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Answer 1 · 2018-03-12T19:23:10

$1/7$

Denoting

$(2, 2)$ by $(x_1, y_1)$

and

$(3, -5)$ by $(x_2, y_2)$

The slope of the line is the rise (difference between $y$ values) divided by the run (difference between $x$ values).

Denoting the slope by $m$

$m = (y_2 - y_1)/(x_2 - x_1)$

$= (-5 - 2)/(3 - 2)$

$= -7/1$

that is

$m = -7$

The slope of a line perpendicular to some other line is the negative reciprocal.

Denoting the required slope by $m'$

$m' = -1/m = - 1/(-7) = 1/7$

What is the slope of any line perpendicular to the line passing through (2,2)(2,2) and (3,-5)(3,-5)?