# CAT 2017 Question Paper | Quants Slot 1

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

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Question 30 : The shortest distance of the point ($$frac{1}{2}$,1) from the curve y = |x - 1| + |x + 1| is 1. 1 2. 0 3. √2 4. √$\frac{3}{2}$ ## 2IIM : Best Online CAT Coaching #### 2IIM's Online CAT CoachingGet CAT Last Mile Prep Course for 799 /-CAT Online Coaching ### Video Explanation ## Best CAT Coaching in Chennai #### CAT Coaching in Chennai - CAT 2020Starts Sat, November 2nd, 2019 ### Explanatory Answer ##### Method of solving this CAT Question from Coordinate Geometry We have to find the shortest distance of the point$$$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 ###### 2IIM's Online CAT CoachingGet CAT Last Mile Prep Course for 799 /- Signup Now! ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2020Enroll at 44,000/- Next Weekend Batch Starts Sat, Nov 2nd, 2019 ###### Best CAT Coaching in ChennaiRegister Online, get Rs 4000/- off Attend a Demo Class ##### 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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