Given a point ( 2,1 ). If the minimum perimeter of a triangle with one vertex at ( 2,1 ), one on the x -axis, and one on the line y = x , is k , then [ k ] is equal to (where [ ] denotes the greatest

Question

Given a point ( 2,1 ). If the minimum perimeter of a triangle with one vertex at ( 2,1 ), one on the x -axis, and one on the line y = x , is k , then [ k ] is equal to (where [ ] denotes the greatest integer function)

TestHub · Accepted Answer

Let, D = ( 2 , − 1 ) be the reflection of A in x -axis, and let E = ( 1 , 2 ) be the reflection in the line y = x . Then A B = B D and A C = CE , so the perimeter of A BC is D B + BC + CE ≥ D E = 1 + 9 ​ = 10 ​

Mathematics - Straight Lines Question with Solution | TestHub

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