# CAT Quantitative Aptitude Questions | Questions for CAT - Coordinate Geometry

###### CAT Questions | CAT Coordinate Geometry | Geometric Probability CAT Questions

The question is from CAT Coordinate Geometry. It combines coordinate geometry with probability. Our task is to find out the probability of abscissa of a given point being greater than 2. A sample space can be described as a region. This region can be defined using coordinate geometry. This fabulous question does both. 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. CAT exam does test one on ideas from CAT Coordinate Geometry once in a while.

Question 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. $$frac{1}{4}\\$ 2. $\frac{1}{3}\\$ 3. $\frac{1}{5}\\$ 4. $\frac{1}{2}\\$ ## Best CAT Online Coaching Try upto 40 hours for free Learn from the best! #### 2IIM : Best Online CAT Coaching. ## Best CAT Coaching in Chennai #### CAT Coaching in Chennai - CAT 2022Limited Seats Available - Register Now! ### Explanatory Answer ##### Method of solving this CAT Question from CAT Coordinate Geometry : A sample space can be described as a region. This region can be defined using coordinate geometry. This fabulous question does both. 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 = $$frac{1.5}{6}\\$ = $\frac{1}{4}\\$ The question is "Given that a point P with coordinates$r, s) lies within the region R, what is the probability that r > 2?"

##### Hence, the answer is $$frac{1}{4}\\$. Choice A is the correct answer. ###### Prepare for CAT 2023 with 2IIM's Daily Preparation Schedule ###### Know all about CAT Exam Syllabus and what to expect in CAT ###### Best CAT Online Coaching Try upto 40 hours for free Learn from the best! ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2023 Classroom Batches Starting Now! @Gopalapuram ###### Best CAT Coaching in Chennai Introductory offer of 5000/- Attend a Demo Class ###### Best Indore IPM & Rohtak IPM CoachingSignup and sample 9 full classes for free. Register now! ## CAT Preparation Online | CAT Geometry - Trigonometry Videos On YouTube #### Other useful sources for Geometry Questions | Coordinate Geometry Questions ##### Where is 2IIM located? 2IIM Online CAT Coaching A Fermat Education Initiative, 58/16, Indira Gandhi Street, Kaveri Rangan Nagar, Saligramam, Chennai 600 093 ##### How to reach 2IIM? Phone:$91) 44 4505 8484
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