CAT Practice : Coordinate Geometry

A sample space can be described as a region. This region can be defined using coordinate geometry. This fabulous question does both.

Coordinate Geometry and Probability

    Q.2: Region R is defined as the region in the first quadrant satisfying the condition 3x + 4y < 12. Given that a point P with coordinates (r, s) lies within the region R, what is the probability that r > 2?


  • Correct Answer
    Choice A.

Detailed Solution

Line 3x + 4y =12 cuts the x-axis at (4, 0) and y axis at (0, 3).

The region in the first quadrant satisfying the condition 3x + 4y < 12 forms a right triangle with sides 3, 4 and 5. Area of this triangle = 6 sq.units.

The lines x = 2 and 3x + 4y = 12 intersect at (2, 1.5). So, the region r > 2, 3x + 4y < 12 also forms a right triangle. This right triangle has base sides 2, 1.5. Area of this triangle = 1.5.

Probability of the point lying in said region =

Correct Answer:

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More questions from Coordinate Geometry

  1. Straightline Shortest distance
  2. Coordinate Geometry and Probability
  3. Cogeo and greatest integer function
  4. Angle bisector theorem
  5. Area under curve
  6. Area of segment
Take Geometry, add one unit of algebra; take a diagram, explain it with x's and y's. For the purists, it is geometry without the romance, for the pragmatists it is Geometry with expanded scope.