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In triangle ABC, angle B is right angled...

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

A

`(1/2)`

B

`sqrt(5/(2))`

C

`(5)/(sqrt2)`

D

`(1)/(sqrt2)`

Text Solution

Verified by Experts

The correct Answer is:
B
`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)`
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