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In triangle ABC angle B is right angled. $A C = 2$ and $A (2, 2)$ , $B (1, 3)$ then the length of the median AD is

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$\frac{1}{\sqrt{2}}$

$\sqrt{\frac{5}{2}}$

$\frac{5}{\sqrt{2}}$

$\frac{1}{2}$

answer is B.

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Detailed Solution

$b = A C = 2, c = A B = \sqrt{2}, a = \sqrt{2}$
$A D = \frac{1}{2} \sqrt{2 b^{2} + 2 c^{2} - a^{2}}$
$A D = \frac{1}{2} \sqrt{8 + 4 - 2} = \sqrt{\frac{10}{4}} = \sqrt{\frac{5}{2}}$

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