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

Options

A. `(1/2)`
B. `sqrt(5/(2))`
C. `(5)/(sqrt2)`
D. `(1)/(sqrt2)`

Answer

B

Explanation

`AB=sqrt(2), AC=2,BC=sqrt(2)`
Using Appollonius' theorem, we get
`2(AD^2+BD^2)=AC^2+AB^2`
`therefore2(AD^2+1//2)=4+2`
`therefore AD^2+1//2=3`
`therefore AD^2=5//2`
`therefore AD=sqrt(5/2)`