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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})

Video Explanation

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