# 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?
1. ${1 \over 4}$
2. ${1 \over 3}$
3. ${1 \over 5}$
4. ${1 \over 2}$

Choice A. ${1 \over 4}$

## 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 = ${{1.5 \over 6} = {1 \over 4}}$

Correct Answer: ${1 \over 4}$

## Our Online Course, Now on Google Playstore!

### Fully Functional Course on Mobile

All features of the online course, including the classes, discussion board, quizes and more, on a mobile platform.

### Cache Content for Offline Viewing

Download videos onto your mobile so you can learn on the fly, even when the network gets choppy!

## More questions from Coordinate Geometry

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.