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# 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....

## 1 Answers

10 years ago

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

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