Question

(–5, 2), (3, −6) and (7, 4) are the vertices of a triangle. Find the length of its median through the vertex (3, −6).

Answer 1

Let A(–5, 2), B(3, −6) and C(7, 4) be the vertices of the given triangle.

Let AD be the median through A, BE be the median through B and CF be the median through C.

We know that median of a triangle bisects the opposite side.

Co-ordinates of point F are

`((-5 + 3)/2, (2 - 6)/2) = ((-2)/2, (-4)/2) = (-1, -2)`

Co-ordinates of point D are

`((3 + 7)/2, (-6 + 4)/2) = (10/2, (-2)/2) = (5, -1)`

Co-ordinates of point E are

`((-5 + 7)/2, (2 + 4)/2) = (2/2, 6/2) = (1, 3)`

The median of the triangle through the vertex B(3, −6) is BE

Using distance formula,

`BE = sqrt((1 - 3)^2 + (3 + 6)^2)`

`BE = sqrt(4 + 81)`

`BE = sqrt(85)`

BE = 9.22