Question

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)`?

Answer 1

`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`