question_answer

The coordinates of vertices A, B and C of a triangle ABC are \[(0,-2),\] \[(4,1)\] and \[(0,4)\] respectively. Find the length of the median through B.

A) 1

B) 2

C) 3

D) 4

Correct Answer: D

Solution :

[d] Since BE is the median. So, E is the mid-point of AC.

\[\therefore \]  Coordinates of E are

\[\left( \frac{0+0}{2},\frac{-2+4}{2} \right)=(0,1)\]

\[\therefore \] Length of median through \[B=BE\]

\[=\sqrt{{{(0-4)}^{2}}+{{(1-1)}^{2}}}=4\]