Question

The area of the region enclosed by the lines \(y = 2x,2y = x\) and \(x = 2\) (in sq.units) is...

• A. \(1\)
• B. \(2\)
• C. \(3\)
• D. \(4\)

Hint:

The region is a triangle with vertices at the origin, (2,4) and (2,1).

Answer 1

The Correct Option is C

Step 1: Triangle
Vertices $(0,0), (2,4), (2,1)$. Shoelace: $\frac12|0(4-1)+2(1-0)+2(0-4)| = \frac12|2-8| = 3$.

Step 2: Answer
Option (C).

Final Answer:
3. \[ \boxed{\text{(C)}\ 3} \]