Answer:
see explanation
Step-by-step explanation:
(a)
Calculate the slope m of AB using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = A(- 5, 2) and (x₂ ) = B(7, - 2)
m = [tex]\frac{-2-2}{7+5}[/tex] = [tex]\frac{-4}{12}[/tex] = - [tex]\frac{1}{3}[/tex]
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{1}{3} }[/tex] = 3
Thus the slope of a line perpendicular to AB is 3
(b)
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = 3, thus
y = 3x + c ← is the partial equation
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
