# CAT 2017 Question Paper | Quants Slot 1

###### CAT Previous Year Paper | CAT Coordinate Geometry Questions | Question 30

Have you ever tried to find the location of a fly sitting on your wall? Rene Descartes, the person who gave birth to the concept of co-ordinate geometry, did once. Try this problem from co-ordinate geometry which appeared in CAT 2017 question paper. It might help you to connect the dots properly! To find more fun questions from CAT Geometry head out here.

Question 30 : The shortest distance of the point ($$frac{1}{2}$,1) from the curve y = |x - 1| + |x + 1| is 1. 1 2. 0 3. √2 4. √$\frac{3}{2}$ ## Best CAT Online Coaching Try upto 40 hours for free Learn from the best! #### 2IIM : Best Online CAT Coaching. ### Video Explanation ## Best CAT Coaching in Chennai #### CAT Coaching in Chennai - CAT 2022Limited Seats Available - Register Now! ### Explanatory Answer ##### Method of solving this CAT Question from Coordinate Geometry We have to find the shortest distance of the point$$$frac{1}{2}$ , 1) from the curve y = |x - 1| + |x + 1|. let x = $\frac{1}{2}$ , y = |$\frac{1}{2}$ - 1| + |$\frac{1}{2}$ + 1| y = 2 i.e.$$$frac{1}{2}$ , 2) y will be entirely positive ; y = |x - 1| + |x + 1| When x = 1 then$1 , 2) is the point and when x = -1, then (-1 , 2) will be the point.

When x > 1 then x – 1 + x + 1 it becomes 2x
When x < 1 then 1 – x - 1 – x it becomes -2x
From the graph obtained we can see that the shortest distance of the point ($$frac{1}{2}$ , 1) from the curve will be the perpendicular distance and is equal to 1. The question is "The shortest distance of the point$$$frac{1}{2}$,1) from the curve y = |x - 1| + |x + 1| is" ##### Hence, the answer is 1 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! ##### 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? Mobile:$91) 99626 48484 / 94459 38484
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