Question

А(2, −4), В(3, 3) and C(−1, 5) are the vertices of triangle ABC. Find the equation of the median of the triangle through A.

Answer 1

The median through A passes through the midpoint of the opposite side BC.

Using the midpoint formula with В(3, 3) and C(−1, 5):

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

`M = ((3 + (-1))/2, (3 + 5)/2)`

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

∴ M = (1, 4)

Using the slope formula with A(2, −4) and M(1, 4):

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

`m = (4 - (-4))/(1 - 2)`

`m = 8/-1`

∴ m = −8

Using the point-slope formula with point A(2, −4):

y − y₁​ = m(x − x₁​)

y − (−4) = −8(x − 2)

y + 4 = −8x + 16

Let’s rearrange into the general form (Ax + By + C = 0):

8x + y + 4 − 16 = 0

8x + y − 12 = 0

Hence, the equation of the median of the triangle through A is 8x + y − 12 = 0.