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i have following question suppose we have some AB length and have turned it by 90 angle about some arbitrary o point lies on the AB length.after turning AB maps some A'B' length.we should find distances between A and B' if AA'=4 and BB'=10 please help

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If you rotate the length around a point $O$ on $AB$, then distances are preserved, so $A'O=AO$ and $B'O=BO$. So $\triangle AOA'$ and $\triangle BOB'$ are isosceles right triangles. If $BB'=10$, then the legs of $\triangle BOB'$ have length $10/\sqrt{2}$, and similarly the legs of $\triangle AOA'$ have length $4/\sqrt{2}$. So you then have the length of the legs of $\triangle AOB'$, and you can use the pythagorean theorem to find the distance $AB'$.

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thank you very much @yunone –  dato datuashvili May 29 '11 at 6:50
    
Glad to help. ${}$ –  yunone May 29 '11 at 6:51

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