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# What is the shortest distance from the point (1/2, 1) to the curve rep

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Math Expert
Joined: 02 Sep 2009
Posts: 64240
What is the shortest distance from the point (1/2, 1) to the curve rep  [#permalink]

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02 Apr 2020, 09:56
00:00

Difficulty:

85% (hard)

Question Stats:

44% (02:22) correct 56% (02:25) wrong based on 57 sessions

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What is the shortest distance from the point (1/2, 1) to the curve represented by $$y = |x - 1| + |x + 1|$$ ?

A. 0
B. 1
C. $$\sqrt{2}$$
D. 1.5
E. 2

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Joined: 14 Oct 2019
Posts: 405
Location: India
GPA: 4
WE: Engineering (Energy and Utilities)
Re: What is the shortest distance from the point (1/2, 1) to the curve rep  [#permalink]

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02 Apr 2020, 10:40
1
the shortest distance from the point (1/2, 1) to the curve represented by y=|x−1|+|x+1| is 1 .
case I : x≥0 , y = x-1+x+1 = 2x
case II : -1<x<1 , y = 1-x+x+1 = 2
case III : x ≤ 0 , y=1-x-1-x = -2x

so the shortest distance will be the perpendicular on the line y=2 ( parallel to x axis ) from point (1/2, 1) = 1

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Re: What is the shortest distance from the point (1/2, 1) to the curve rep   [#permalink] 02 Apr 2020, 10:40