Question

Determine the equation of the altitude from A.

Answer 1

Answer:

y = - 3x + 11

Step-by-step explanation:

the altitude is a line from the vertex A drawn perpendicular to the opposite side BC

calculate the slope of BC using the slope formula

m = $\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

with (x₁, y₁ ) = B (- 7, 3 ) and (x₂, y₂ ) = C (- 1, 5 )

$m_{BC}$ = $\frac{5-3}{-1-(-7)}$ = $\frac{2}{-1+7}$ = $\frac{2}{6}$ = $\frac{1}{3}$

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 ) , then

y = - 3x + c ← is the partial equation

to find c substitute A (4, - 1 ) into the partial equation

- 1 = - 12 + c ⇒ c = - 1 + 12 = 11

y = - 3x + 11 ← equation of altitude from A