What is the slope of a line that is perpendicular to V(3, 2), W(8, 5)?

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Answer 1 · 2018-04-02T10:00:44

See a solution process below:

The formula for find the slope of a line is:

$m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))$

Where $(color(blue)(x_1), color(blue)(y_1))$ and $(color(red)(x_2), color(red)(y_2))$ are two points on the line.

Substituting the values from the points in the problem gives:

$m = (color(red)(5) - color(blue)(2))/(color(red)(8) - color(blue)(3)) = 3/5$

Let's call the slope of a perpendicular line: $color(blue)(m_p)$

The slope of a line perpendicular to a line with slope $color(red)(m)$ is the negative inverse, or:

$color(blue)(m_p) = -1/color(red)(m)$

Substituting the slope for the line in the problem gives:

$color(blue)(m_p) = (-1)/color(red)(3/5) = -5/3$