# 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. $\frac{1}{2}\\$ ## Rs. 2500 off on 2IIM Ultimate DI LR Course for CAT 2019. Offer valid till March 24th. #### Signup to sample the Best CAT Online Coaching ## Best CAT Coaching in Chennai #### Starts Sat, Mar 23, 2019 ### 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. ###### Online CAT CoachingTry it free! Register in 2 easy steps and start learning in 30 seconds! ###### Already have an Account? ###### CAT Coaching in Chennai Next Weekend Batch Starts Sat, Mar 23rd, 2019 ###### Best CAT Coaching in Chennai Sign up for a Free Demo of our CAT Coaching in Chennai ## 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, 10-C, Kalinga Colony, Bobbili Raja Salai K.K.Nagar, Chennai. India. Pin - 600 078 ##### How to reach 2IIM? Phone:$91) 44 4505 8484
Mobile: (91) 99626 48484
WhatsApp: WhatsApp Now
Email: prep@2iim.com