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

Question

1750 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-12T19:23:10

$\frac{1}{7}$ $1/7$

Denoting

$(2, 2)$ $(2, 2)$ by $(x_{1}, y_{1})$ $(x_1, y_1)$

and

$(3, - 5)$ $(3, -5)$ by $(x_{2}, y_{2})$ $(x_2, y_2)$

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

Denoting the slope by $m$ $m$

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ $m = (y_2 - y_1)/(x_2 - x_1)$

$= \frac{- 5 - 2}{3 - 2}$ $= (-5 - 2)/(3 - 2)$

$= - \frac{7}{1}$ $= -7/1$

that is

$m = - 7$ $m = -7$

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)(2,2) and (3,-5)(3,−5)(3,-5)?