Question

Find the equation of the median through A of Δ ABC whose vertices are A(2, 5), B(−4, 9) and C(−2, −1).

Answer 1

A median from vertex A connects to the midpoint of the opposite side BC.

⇒ Using the midpoint formula for B(−4, 9) and C(−2, −1):

`M = ((x_1 + x_2)/2, (y_1 + y_2)/2)`

`M = ((-4 + (-2))/2, (9 + (-1))/2)`

`M = ((-6)/2, 8/2)`

∴ M = (−3, 4)

⇒ The median passes through A(2, 5) and M(−3, 4), using the slope formula:

`m = (y_2 - y_1)/(x_2 - x_1)`

`m = (4 - 5)/(-3 - 2)`

`m = (-1)/(-5)`

∴ `m = 1/5`

⇒ Using the point-slope formula with `m = 1/5` with point A(2, 5):

y − y₁ = m(x − x₁)

`y - 5 = 1/5 (x - 2)`

5(y − 5) = x − 2

5y − 25 = x − 2

x − 5y + 23 = 0

Hence, the equation of the median is x − 5y + 23 = 0.