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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) #?

1 Answer

Jun 4, 2016

#6y=11x#

Explanation:

A line through #(9,2)# and #(-2,8)# has a slope of
#color(white)("XXX")m_1=(8-2)/(-2-9)=-6/11#

All lines perpendicular to this will have a slope of
#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:
#color(white)("XXX")(y-0)/(x-0)=11/6#
or
#color(white)("XXX")6y=11x#

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