CAT 2017 Question Paper | Quants Slot 1

CAT Questions

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})

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Video Explanation

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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