Question

A is the point (8,3) and B is the point (12, 1).

Find the equation of the line, perpendicular to the line AB, which passes through the point (0,0).

Answer 1

y = 2x

Explanation:

calculate the slope of AB using the slope formula

m =
`(y_(2) -y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = A (8, 3) and (x₂, y₂ ) = B (12, 1 )

`m_(AB)` =
`(1-3)/(12-8)` =
`(-2)/(4)` = -
`(1)/(2)`

given a line with slope m then the slope of a line perpendicular to it is

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/(-(1)/(2) )` = 2

the equation of a line passing through the origin (0, 0 ) is

y = mx

here m = 2 , then

y = 2x ← equation of perpendicular line