Question

If A(1, 4), B(3, 0) and C(2, 1) are the vertices of a triangle, then the length of the median through C is

Answer 1

Given:

A(1, 4)

B(3, 0)

C(2, 1)

The median through the vertex C will meet at the mid point of AB.

Coordinate of mid-point on AB=  $(\frac{1+3}{2},\frac{4+0}{2} )$

$=(\frac{4}{2}, \frac{4}{2} )$

=(2,2)

Length of median through vertex C= Distance between (2, 1) and (2,2)

Length of median

$=\sqrt{(2-2)^{2}+(2-1)^{2} } \\=\sqrt{0+1^{2} } \\=\sqrt{1^{2} }$

=1 unit

Hence the length of median through the vertex C is 1 units.