Question

A(5, 4), B(−3, −2) and C(1, −8) are the vertices of a triangle ABC. Find:

1. the slope of the altitude of AB,
2. the slope of the median AD and
3. the slope of the line parallel to AC.

Answer 1

Given, A(5, 4), B(−3, −2) and C(1, −8) are the vertices of a triangle ABC.

i. Slope of AB = `(-2 - 4)/(-3 - 5) = (-6)/(-8) = 3/4`

Slope of the altitude of AB = `(-1)/"slope of AB" = (-1)/(3/4) = (-4)/3`

ii. Since, D is the mid-point of BC.

Co-ordinates of point D are `((-3 + 1)/2, (-2 - 8)/2) = (-1, -5)`

Slope of AD = `(-5 - 4)/(-1 - 5) = (-9)/(-6) = 3/2`

iii. Slope of AC = `(-8 - 4)/(1 - 5) = (-12)/(-4) = 3`

Slope of line parallel to AC = Slope of AC = 3