Question

O(0, 0), A(3, 5) and B(−5, −3) are the vertices of triangle OAB. Find the equation of median of triangle OAB through vertex O.

Answer 1

Let the median through O meets AB at D.

So, D is the mid-point of AB.

Co-ordinates of point D are

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

Slope of OD = `(1 - 0)/(-1 - 0) = -1`

(x₁, y₁) = (0, 0)

The equation of the median OD is

y – y₁ = m(x – x₁)

y − 0 = −1(x − 0)

x + y = 0