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M10: Q27 - DS

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Re: M10: Q27 - DS [#permalink] New post 14 Sep 2011, 16:59
balboa wrote:
Is point A closer to point (1, 2) than to point (2, 1) ?

1. Point A lies on the line y = x
2. Point A lies on the line y = -x

[Reveal] Spoiler: OA
A

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Both Statement together not sufficient.
The Answer is E.
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Re: M10: Q27 - DS [#permalink] New post 05 Jul 2012, 03:46
If this question were about the distance between line x =y and point A, then the distance that we need to consider between the point and the line is the perpendicular distance between the line and the point?

Also, when considering distance between two points, say point (2,1) and point A on the line, this distance between two points is not necessarily perpendicular.?
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Re: M10: Q27 - DS [#permalink] New post 05 Jul 2012, 03:54
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teal wrote:
If this question were about the distance between line x =y and point A, then the distance that we need to consider between the point and the line is the perpendicular distance between the line and the point?

Also, when considering distance between two points, say point (2,1) and point A on the line, this distance between two points is not necessarily perpendicular.?


Yes, the distance between a point and a line is the length of the perpendicular from that point to the line.

As for the distance between two points: the distance between two points is the length of the line segment from one point to another. So, "perpendicular distance from one point to another" does not make ANY sense.

For more check Coordinate Geometry chapter of Math Book: math-coordinate-geometry-87652.html

Hope it helps.
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Re: M10: Q27 - DS [#permalink] New post 05 Jul 2012, 04:21
serious brain freeze on my part .....perpendicular distance between two points ( what a joke) God man!
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Re: M10: Q27 - DS [#permalink] New post 12 Sep 2012, 05:03
Bunuel has given the best approach to get the right answer.

at line y=x , any point will be equi distance from the given two points at the same time.
at y=-x , it is not possible to get.

A wins
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Re: M10: Q27 - DS [#permalink] New post 12 Sep 2012, 07:07
balboa wrote:
Is point A closer to point (1, 2) than to point (2, 1) ?

1. Point A lies on the line y = x
2. Point A lies on the line y = -x

[Reveal] Spoiler: OA
A

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A relevant geometrical property:

A point is equally distant from the endpoints of a given line segment if and only if it belongs to the perpendicular bisector of the line segment.
(You can see it if you draw the perpendicular bisector that each point on it, together with the two endpoints of the line segment, they form an isosceles triangle).

In our case, M(1,2) and N(2,1) define a line segment. The slope of the line going through MN is -1, therefore the line y = x is perpendicular to MN.
The midpoint of MN has coordinates ((1+2)/2,(2+1)/2)=(3/2,3/2) which lies on the line y = x. So, y = x is the perpendicular bisector of MN.

From the above, it follows that Statement (1) is sufficient, as each point on the line y = x is equally distant from M and N.

Statement (2): the line y = -x is parallel to the line segment MN. Except for one point on this line (which also belongs to the line y = x), any point A on the line y = -x will be closer to one of the endpoints of MN, and there are infinitely many points closer to either end of MN. Thus, not sufficient.

Answer A
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Re: M10: Q27 - DS [#permalink] New post 11 Sep 2013, 16:39
I made the silly mistake of finding the distance between (1,2) and the line, similarly (2,1) from the line. Giving the answer to be D but reading through the posts, A makes sense, as we are trying to find the distance between the two given points and a point 'A' anywhere on the line.
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Re: M10: Q27 - DS [#permalink] New post 11 Sep 2013, 22:57
I would have said C because we need both equations to determine the fact that A is on a line that passes by the origin!

Buy thanks Brunel for your explanation it was really clear!
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Re: M10: Q27 - DS [#permalink] New post 27 Aug 2014, 02:27
My answer is A.

1st option is sufficient as the points will be at same distance from A.
2nd option is not sufficient as we can't exactly say if A is on the line y = -x then which one is closer.
Re: M10: Q27 - DS   [#permalink] 27 Aug 2014, 02:27
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