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paradox xyz cool Grade: 11
        

A triangle has two of its vertices at P(a,0) and Q(0,b) and the third vertex R(x,y) is moving along the straight line y=x. If A be the area of triangle, then dA/dx is equal to?


I know the answer it is " -(a+b)/2"  but I dont know know how to solve the problem.


Plz explain the solution....

6 years ago

Answers : (1)

vikas askiitian expert
510 Points
										

let R be any point (X,Y)


since this point  lies on line Y = X so


 R =(X,X)


 p=(a,0)


q=(0,b)


now by determinant method area = 1/2 (determinant)


                                            A   =1/2 [ab - X(a+b)]


differentiating wrt X


                   dA/dx = 1/2 . -(a+b)


                            =-(a+b)/2


 

6 years ago
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