Question

Find the length of the median from the vertex B of ∆ABC whose vertices are A(1, -1), B(0, 4) and C(-5, 3)

Answer 1

`√(13)`

Explanation:

The median from B intersects the midpoint of AC

Find the midpoint using the midpoint formula

midpoint = [ 0.5(1 - 5), 0.5(- 1 + 3) ] = (- 2, 1 )

Calculate the length using the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = - 2, 1 ) and (x₂, y₂ ) = (0, 4 )

d =
`√((0+2)^2+(4-1)^2)`

=
`√(2^2+3^2)`

=
`√(4+9)` =
`√(13)` ≈ 3.6 ( to 1 dec. place )