Question

If A (2, 2), B (−4, −4) and C (5, −8) are the vertices of a triangle, than the length of the median through vertex C is

(a) $\sqrt{65}$

(b) $\sqrt{117}$

(c) $\sqrt{85}$

(d) $\sqrt{113}$

Answer 1

We have a triangle in which the co-ordinates of the vertices are A (2, 2) B (−4,−4) and C (5,−8).

In general to find the mid-point of two points and we use section formula as,

Therefore mid-point D of side AB can be written as,

Now equate the individual terms to get,

So co-ordinates of D is (−1,−1)

So the length of median from C to the side AB,

So the answer is (c)