Question

Find the equation of the line passing through point A and perpendicular to AB ?

Answer 1

Answer:

see explanation

Step-by-step explanation:

(a ) calculate the slope m using the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = A(0, 6) and (x₂, y₂ ) = B(3, 0 )

$m_{AB}$ = $\frac{0-6}{3-0}$ = $\frac{-6}{3}$ = - 2

(b)

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

$m_{perpendicular}$ = - $\frac{1}{m}$ = - $\frac{1}{-2}$ = $\frac{1}{2}$

(c)

the equation of a line in slope- intercept form is

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

(0, 6 ) is the y-intercept ⇒ c = 6

y = $\frac{1}{2}$ x + 6 ← equation of perpendicular line