Question

Find the length of the median through the vertex B of ΔABC with vertices A(9, −2), B(−3, 7) and C(−1, 10).

Answer 1

D is the midpoint of AC.

⇒ D (x, y) = `((9 - 1)/2, (10 - 2)/2)`

⇒ D (x, y) = `(8/2, 8/2)`

⇒ D (x, y) = (4, 4)

⇒ length = 3D

= `sqrt((4 + 3)^2 + (4 - 7)^2)`

= `sqrt(49 + 9)`

= `sqrt58` units.