Question

The vertices of a ΔABC are A(−2, 4), B(4, 3) and C(1, −6). Find length of the median BD.

Answer 1

BD is the median of MBC

∴ D is the mid-point of side AC 

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

`D = ((-2 + 1)/2 , (4 - 6)/2)`

`D = (-1/2, -1)`

BD = `|sqrt((x_3 - x_4)^2 + (y_3 - y_4)^2)|`

BD = `|sqrt(((-1)/2 - 4)^2 + (-1 -3)^2)|`

BD = `|sqrt(81/4 + 16)|`

BD = `sqrt(145/4) = sqrt(145/2)` units