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

Answer:

y = 3x + 11

Step-by-step 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 = $\frac{-2-2}{7+5}$ = $\frac{-4}{12}$ = - $\frac{1}{3}$

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

$m_{perpendicular}$ = - $\frac{1}{m}$ = - $\frac{1}{-\frac{1}{3} }$ = 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