Question

If A (−1, 3), B (1, −1) and C (5, 1) are the vertices of a triangle ABC, find the length of the median through A.

Answer 1

The distance d between two points and is given by the formula

The co-ordinates of the midpoint between two points and is given by,

Here, it is given that the three vertices of a triangle are A(−1,3), B(1,−1) and C(5,1).

The median of a triangle is the line joining a vertex of a triangle to the mid-point of the side opposite this vertex.

Let ‘D’ be the mid-point of the side ‘BC’.

Let us now find its co-ordinates.

Thus we have the co-ordinates of the point as D(3,0).

Now, let us find the length of the median ‘AD’.

Thus the length of the median through the vertex ‘A’ of the given triangle is.