Question

Let $B\equiv(0,3)$ and $C\equiv(4,0)$. The point A is moving on the line $y=2x$ at the rate of 2 units/second. The area of $\triangle ABC$ is increasing at the rate of

• A. $\frac{11}{\sqrt{5}}(units)^{2}/sec$
• B. $\frac{11}{5}(units)^{2}/sec$
• C. $\frac{13}{\sqrt{5}}(units)^{2}/sec$
• D. $\frac{13}{5}(units)^{2}/sec$

Hint:

Calculus Tip: When a point moves along a specific curve or line at a given speed, always express its position parametrically using a single variable (like $h$) and use the distance formula from a fixed point (usually the origin) to link the speed to the derivative of that parameter ($\frac{dh}{dt}$).

Answer 1

The Correct Option is A