If two lines l and m have equations -x+6, and y = -4x+6, what is the probability that a point randomly selected in the 1st quadrant and below l will fall between l and m? Express your answer as a decimal to the nearest hundredth.

supremecheetah May 30, 2023

#1**0 **

The lines l and m intersect at the point (3, 0). The area of the triangle formed by the lines l, m, and the x-axis is (1/2)(3)(6) = 9. The area of the rectangle formed by the lines l, m, and the y-axis is (3)(6) = 18. The probability that a point randomly selected in the 1st quadrant and below l will fall between l and m is the ratio of the area of the triangle to the area of the rectangle, or 9/18 = 1/2. To the nearest hundredth, this is 0.50.

Guest May 31, 2023