Differentiation Question 123
Question: A triangle has two of its vertices at $ P(a,0),Q(0,b) $ and the third vertex $ R(x,y) $ is moving along the straight line $ y=x. $ If A be the area of the triangle. Then $ \frac{dA}{dx} $ is equal to
Options:
A) $ \frac{a-b}{2} $
B) $ \frac{a-b}{4} $
C) $ =-( \frac{a+b}{2} ) $
D) $ \frac{a+b}{4} $
Show Answer
Answer:
Correct Answer: C
Solution:
[c] Area of $ \Delta PQR=A $
$ =\frac{-1}{2}[x(b-0)+0(0-y)+a(y-b)] $
$ =\frac{-1}{2}(bx+ax-ab) $
$ \therefore \frac{dA}{dx}=\frac{-1}{2}(a+b) $
BETA
