Question

Find the length of the medians of a ΔABC having vertices at A(0, −1), B(2, 1) and C(0, 3).

Answer 1

We have to find the lengths of the medians of a triangle whose co-ordinates of the vertices are A (0,−1); B (2, 1) and C (0, 3).

So we should find the mid-points of the sides of the triangle.

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

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

Now equate the individual terms to get,

So co-ordinates of P is (1, 0)

Similarly mid-point Q of side BC can be written as,

Now equate the individual terms to get,

So co-ordinates of Q is (1, 2)

Similarly mid-point R of side AC can be written as,

Now equate the individual terms to get,

So co-ordinates of R is (0, 1)

Therefore length of median from A to the side BC is,

Similarly length of median from B to the side AC is,

Similarly length of median from C to the side AB is