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# Point (1,0) is closest to which of the following lines? A.

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Manager
Joined: 14 Jun 2009
Posts: 87
Point (1,0) is closest to which of the following lines? A.  [#permalink]

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Updated on: 15 Jun 2014, 02:31
1
12
00:00

Difficulty:

55% (hard)

Question Stats:

60% (01:03) correct 40% (01:11) wrong based on 413 sessions

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Point (1,0) is closest to which of the following lines?

A. y = x
B. y = 1
C. y + x = 3
D. x = 2
E. x + y = −1

M24-34

Originally posted by arvs212 on 11 Aug 2009, 21:24.
Last edited by Bunuel on 15 Jun 2014, 02:31, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
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Re: point (1,0) is closest to which line?  [#permalink]

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11 Aug 2009, 22:34
It is easier to draw the point and lines.

1) y=x - a half of the diagonal of 1*1 square: 1/\sqrt{2}
2)y=1 - 1
3)y+x=3 - goes too far, definitely >1
4)x=2 - 1
5)x+y=-1 - goes too far, definitely >1
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Manager
Joined: 27 Oct 2008
Posts: 180
Re: point (1,0) is closest to which line?  [#permalink]

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25 Sep 2009, 23:14
Soln. I too agree with answer A. Drawing the quadrants and trying to plot the lines approximately i suppose will help to solve this problem.
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Location: India
Schools: South Asian B-schools
Re: point (1,0) is closest to which line?  [#permalink]

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26 Sep 2009, 05:04
my approach is just visualize each line in mind
( i know its easier said than done...but considering 2 mins time....i think this is the fastest way)
refer image attached.......Now the task is to find min distance from a line in options to the point (1,0).......this can also be done by a formula from a geometry chapter

First visualise point (1,0)...now to calculate min distance....here its very helpful to know a property.....in 45-45-90 triangle.....sides are in 1:1:srt(2) proportion....now apply this in following options

1) y=x....since y=x.....aangle of line wrto x axis = 45 ( shown in fig)....we need perpendicular distance hence another angle = 90 deg....thus it becomes a triangle of 45-45-90....hence hypoteneous is 1...now equate the proportion as 1:1:srt(2) = x:x:1.....this gives x = 1/srt(2)min distance = 1/srt(2)

2)y=1....min distance = 1
3)y+x=3......min distance = srt(2).......apply the same logic as of option 1
4)x=2.....min distance = 1
5)x+y=-1....min distance = srt(2).......apply the same logic as of option 1

OA A
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Re: point (1,0) is closest to which line?  [#permalink]

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26 Sep 2009, 12:37
3
i hope now i m clear
Attachments

untitled.JPG [ 23 KiB | Viewed 4638 times ]

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Re: point (1,0) is closest to which line?  [#permalink]

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02 Jan 2013, 23:00
2
arvs212 wrote:
point (1,0) is closest to which line?

1) y=x
2)y=1
3)y+x=3
4)x=2
5)x+y=-1

Best approach is to sketch the lines.
Practice getting the y-intercept and the x-intercepts.
These two intercepts will guide you win in sketching your lines.

1) (0,0) (1,1) (2,2) ... (n,n)
2) draw a line that intersects y=1 (This is quickly beaten by y=x. OUT!)
3) (0,3) (3,0) (This is quickly beaten by y=x. OUT!)
4) draw a line that intersects x=2
5) (0,-1) (-1,0) (This is quickly beaten by y=x. OUT!)

Looking at the scetch you will notice that (4) x=2 has a minimum distance of 1.
Looking at the scetch of (1) x=y has a minimum distance of d < 1
Attachments

lines.jpg [ 31.23 KiB | Viewed 4010 times ]

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Point (1,0) is closest to which of the following lines? A.  [#permalink]

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15 Jun 2014, 02:32
1
1
arvs212 wrote:
Point (1,0) is closest to which of the following lines?

A. y = x
B. y = 1
C. y + x = 3
D. x = 2
E. x + y = −1

M24-34

Look at the diagram below:

As you can see point (1,0) is closest to line y = x.

Attachment:

Untitled.png [ 15.99 KiB | Viewed 3219 times ]

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Re: Point (1,0) is closest to which of the following lines? A.  [#permalink]

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16 Dec 2017, 06:17
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Re: Point (1,0) is closest to which of the following lines? A. &nbs [#permalink] 16 Dec 2017, 06:17
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