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What is the equation of the line that passes through the origin and is perpendicular to the line that passes through the following points: $(9, 2), (- 2, 8)$ $(9,2),(-2,8)$ ?

1 Answer

Jun 4, 2016

$6 y = 11 x$ $6y=11x$

Explanation:

A line through $(9, 2)$ $(9,2)$ and $(- 2, 8)$ $(-2,8)$ has a slope of
$XXX m_{1} = \frac{8 - 2}{- 2 - 9} = - \frac{6}{11}$ $color(white)("XXX")m_1=(8-2)/(-2-9)=-6/11$

All lines perpendicular to this will have a slope of
$XXX m_{2} = - \frac{1}{m_{1}} = \frac{11}{6}$ $color(white)("XXX")m_2=-1/m_1=11/6$

Using the slope-point form, a line through the origin with this perpendicular slope will have an equation:
$XXX \frac{y - 0}{x - 0} = \frac{11}{6}$ $color(white)("XXX")(y-0)/(x-0)=11/6$
or
$XXX 6 y = 11 x$ $color(white)("XXX")6y=11x$

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