GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 24 May 2020, 18:59

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 64068
What is the shortest distance from the point (1/2, 1) to the curve rep  [#permalink]

### Show Tags

02 Apr 2020, 09:56
00:00

Difficulty:

85% (hard)

Question Stats:

45% (02:22) correct 55% (02:21) wrong based on 56 sessions

### HideShow timer Statistics

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

_________________
Senior Manager
Joined: 14 Oct 2019
Posts: 403
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]

### Show Tags

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

Attachments

shortest distance.jpg [ 1.45 MiB | Viewed 494 times ]

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