Question

Q.1
(a) A (-3,1 ), B (4,4) and C(1,-2) are the vertices of triangle ABC.
Find:
(i) The equation of median BD.
(ii) The equation of altitude AE.​

Answer 1

I) The equation of median BD is y = x/3 +8/3.

II) The equation of altitude AE is y = -x/2 - 1/2.

Given the vertices of the triangle A (-3,1 ), B (4,4) and C(1,-2).

The point D is the midpoint of the line AC . The coordinates of the D are ((-3+1)/2 , (1-2)/2) = (-2,-1/2).

Slope of median BD = (4+1/2)/(4+2) = 1/3

Equation of median BD-

y - 4 = 1/3(x-4)

=> y = x/3 +8/3

The altitude AE is perpendicular to the line BC.

Slope of AE = -1/slope of BC

Slope of BC = (4+2)/(4-1) = 2

Slope of AE = -1/2

Equation of the altitude AE -

y - 1 = -1/2(x + 3)

=> y = -x/2 - 1/2