Two straight lines pass through the origin (x_0, y_0) = (0, 0). One of them passes through the point (x_1, y_1) = (1, 3) and the other passes through the point (x_2, y_2) = (1, 2). What is the area enclosed between the straight lines in the interval [0, 1] on the x-axis? A. 0.5 B. 1.0 C. 1.5 D. 2.0

GATE 2022 · General Aptitude · Cartesian Coordinates · medium

Answer: Area enclosed between y=3x and y=2x over [0,1] = 0.5. Answer: A. 0.5.

1. Find equations of both lines: Line through (0,0) and (1,3): slope = 3/1 = 3, so y = 3x. Line through (0,0) and (1,2): slope = 2/1 = 2, so y = 2x.
2. Set up the area integral: For x in [0,1]: 3x >= 2x, so the upper curve is y=3x and lower is y=2x. Area = integral from 0 to 1 of x dx.
3. Evaluate the integral: Area = [x^2/2] evaluated from 0 to 1 = 1/2 - 0 = 0.5.