Question

A (-5,2) B (7,-2) C (-2,5) find the equation of the line perpendicular to line AB and passing throught point C

Answer 1

y = 3x + 11

Explanation:

Calculate the slope of AB using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = A(- 5, 2) and (x₂, y₂ ) = B(7, - 2)

m =
`(-2-2)/(7+5)` =
`(-4)/(12)` = -
`(1)/(3)`

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

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/(-(1)/(3) )` = 3

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept ), thus

y = 3x + c ← partial equation of perpendicular line

To find c substitute C(- 2, 5) into the partial equation

5 = - 6 + c ⇒ c = 5 + 6 = 11

y = 3x + 11 ← equation of perpendicular line