Question

Determine the equation of the altitude from A.

Answer 1

y = - 3x + 11

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 =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

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

`m_(BC)` =
`(5-3)/(-1-(-7))` =
`(2)/(-1+7)` =
`(2)/(6)` =
`(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 ) , 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