Question

A(5,4) , b(-3,-2) and c(1,-8) are the vertices of triangle abc find the equation of median ad and line parallel to ac passing through point b

Answer 1

Answer:

3x - 2y - 7 = 0 ; 3x – y + 7 = 0

Step-by-step explanation:

Given,

A = (5,4), B = (-3, -2), C =  (1, -8)

Segment AD is median. D is midpoint of BC.

x = x₁ + x₂ / 2 = -3 + 1/2 = -1.

y = y₁ + y₂/2 = -2 - 8 /2 = -5.

D = (-1,-5)

Equation of Median AD where A(5,4), D(-1,-5) :

y - y₁ = m (x - x₁) where m = y₂ - y₁ / x₂ - x₁

m = -5 -4 / -1 -5 = 9/6.

y - 4 = 9/6(x - 5)

6y - 24 = 9x - 45

9x - 6y - 21 = 0.

3x - 2y - 7 = 0

Therefore the equation of median AD = 3x - 2y - 7 = 0.

Slope of Line AC = y₂ - y₁/x₂ - x₁ = -8 -4 /1 -5 = -12/-4 = 3.

Since the line BP is parallel to AC, The slope of BP will be same as that of AC.

equation of BP

y - y₁ = m(x - x₁)

y + 2 = 3(x + 3)

3x  - y + 7 = 0

Therefore the equation of line BP = 3x – y + 7 = 0