What is the slope of any line perpendicular to the line passing through $(14, 2)$ $(14,2)$ and $(9, 5)$ $(9,5)$ ?

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Answer 1 · 2015-12-30T12:54:59

The slope of the perpendicular is $\frac{5}{3}$ $5/3$ The explanation is given below.

Slope $m$ $m$ of any line passing through two given points $(x_{1}, y_{1})$ $(x_1,y_1)$ and $(x_{2}, y_{2})$ $(x_2,y_2)$ is given by

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

The slope of perpendicular would be negative reciprocal of this slope.

$m_{p} = - \frac{x_{2} - x_{1}}{y_{2} - y 1}$ $m_p = -(x_2-x_1)/(y_2-y1)$

Our given points are $(14, 2)$ $(14,2)$ and $(9, 5)$ $(9,5)$

$x_{1} = 14$ $x_1=14$ , $y_{1} = 2$ $y_1=2$
$x_{2} = 9$ $x_2=9$ , $y_{2} = 5$ $y_2=5$

The slope of any line perpendicular to the line joining $(14, 2)$ $(14,2)$ and $(9.5)$ $(9.5)$ is given by.

$m_{p} = - \frac{9 - 14}{5 - 2}$ $m_p = -(9-14)/(5-2)$
$m_{p} = - \frac{- 5}{3}$ $m_p = -(-5)/3$
$m_{p} = \frac{5}{3}$ $m_p=5/3$

The slope of the perpendicular is $\frac{5}{3}$ $5/3$

What is the slope of any line perpendicular to the line passing through (14,2)(14,2) and (9,5)(9,5)?