The vertices of a triangle are $A (3, 4), B (7, 2), C (- 2, - 5)$ . Find the length of the median through vertex $A$ .

\frac{\sqrt{122}}{3}

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\frac{\sqrt{142}}{2}

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\frac{\sqrt{142}}{3}

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\frac{\sqrt{122}}{2}

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Solution

The correct option is D $\frac{\sqrt{122}}{2}$
Clearly, Median Through A will meet the line BC

So, mid point of $B C = (\frac{5}{2}, \frac{- 3}{2})$

Now, length of Median= $\sqrt{(3 - \frac{5}{2})^{2} + (4 + \frac{3}{2})^{2}} = \frac{\sqrt{122}}{2}$

Therefore, Answer is $D$

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Question 122

The angles of a triangle are in the ratio 2 : 3 : 5. Find the angles.

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