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Re: Is point A closer to point (1,2) than to point (2,1) ? [#permalink]

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15 Dec 2007, 15:24

Answer A is right.

The best way to approach this is to draw the points and the lines in a cartesian plane.
With condition 1, each point on the line is equally distant from both the points, therefore it is SUFFICIENT to answer NO

With condition 2, it is simplt to visualize the some points on the line are closer to (1,2) and other points are closer to (2,1)

Re: Is point A closer to point (1,2) than to point (2,1) ? [#permalink]

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29 May 2009, 09:39

1

This post received KUDOS

bmwhype2 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

Is there an algebraic/formula approach to this

A should be it.

1. If point A lies on the line y=x, any point on this line has equal value for x and y and both are either positive or negative. Lets say point A lies on (4, 4).

i. The distance between A and (1, 2 ) = Sqrt {(4-1)^2 + (4-2)^2} = Sqrt {9 + 4 } = Sqrt (13) ii. The distance between A and (2, 1 ) = Sqrt {(4-2)^2 + (4-1)^2} = Sqrt {4 + 9} = Sqrt (13) Both are same.

If point A lies on (-3, -3).

i. The distance between A and (1, 2 ) = Sqrt {(-3-1)^2 + (-3-2)^2} = Sqrt (41) ii. The distance between A and (2, 1 ) = Sqrt {(-3-2)^2 + (-3-1)^2} = Sqrt (41)

Both are equidistance. Suff..

2. If point A lies on the line y=-x, any point other than (0, 0) on this line has different values for x and y i.e. if x is +ve, y is -ve and vice versa. So any point on the line y = -x is not equidistance from point (1,2) and (2,1).

Lets say point A lies on (4, -4).

i. The distance between A and (1, 2 ) = Sqrt {(4-1)^2 + (-4-2)^2} = Sqrt {9 + 36 } = Sqrt (45) ii. The distance between A and (2, 1 ) = Sqrt {(4-2)^2 + (-4-1)^2} = Sqrt {4 + 25} = Sqrt (29)

So these two points are not equidistance from A. NSF. Hence only A is correct.
_________________

Re: Is point A closer to point (1,2) than to point (2,1) ? [#permalink]

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17 Sep 2014, 03:21

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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