Question

If A (4,9),B(2,3) and C(6,5) are the vertices of triangle ABC, then the length of the median through C is _______

Answer 1

Answer:

The answer is $\sqrt{10}$

Step-by-step explanation:

Midpoint of A(4,9) and B(2,3) is $=(\frac{4+2}{2},\frac{9+3}{2})=(3,6)$

Thus the length of median through C

          $=$ distance between C(6,5) and (3,6)

         $=\sqrt{(3-6)^2+(6-5)^2}\\=\sqrt{9+1}=\sqrt {10}$

(Using distance formula $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$)