Question

The points A(-3,6), B(8,6), C(8,-4)and D(-3,-4)are vertices of rectangle ABCD. A point is selected at random from the interior of this rectangle. What is the probability that the x-coordinate of the point is negative and the y-coordinate of the point is positive?

Answer 1

the probability that the x-coordinate of the point is negative and the y-coordinate of the point is positive is 16.36%

Explanation:

Assuming that each point has the same probability to be chosen ( uniform probability distribution in the rectangle area ) then the probability of choosing a negative x-coordinate and positive y-coordinate is the ratio of the area with those requirements over the total area of the rectangle.

therefore

Ar= area of negative x-values and positive y-values = (-3)*6 = 18

AT= total area of the rectangle = [8-(-3) ]*[6-(-4)] = 110

then

probability = Ar/AT = 18/110 = 0.1636 = 16.36%