A rectangle has vertices at the points (9, 6), (9, -9), (-1, -9), and (-1, 6) on the coordinate plane. A circle of radius 5 lies within this rectangle. What is the probability that a random point (x, y) that lies within the rectangle also lies within the circle?

A. 1 – π/6 B. 1/2 C. 25/15π D. π/4 E. π/6

(E) Let's determine the area for the rectangle that has vertices at the points indicated above. A sketch will help you visualize the rectangle.

Its length is the difference between the y coordinates: 6 – (-9) = 15.

Its width is the difference between x coordinates: 9 – (-1) = 10.

The area of the rectangle = 10 × 15 = 150.

The circle, which has a radius of 5, has an area of: π(5²) = 25π.

The question is asking us to find the probability that a point within the rectangle will also lie within the circle. This probability is the area of the circle divided by the area of the rectangle.

Probability = 25π/150 = π/6. The correct answer is choice (E).

Could you, please, draw a sketch for this question?

Users browsing this forum: Google [Bot] and 4 guests

You cannot post new topics in this forum You cannot reply to topics in this forum You cannot edit your posts in this forum You cannot delete your posts in this forum You cannot post attachments in this forum

GMAT(TM) and GMAT CAT (TM) are registered trademarks of the Graduate Management Admission Council(TM). The Graduate Management Admission Council(TM) does not endorse, nor is affiliated in any way with the owner or any content of this site.