In the xy-coordinate plane, is point R equidistant from

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In the xy-coordinate plane, is point R equidistant from [#permalink]

03 Dec 2012, 05:25

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In the xy-coordinate plane, is point R equidistant from points (-3,-3) and (1,-3) ?

(1) The x-coordinate of point R is -1.
(2) Point R lies on the line y = -3.

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Re: In the xy-coordinate plane, is point R equidistant from [#permalink]

03 Dec 2012, 05:32

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In the xy-coordinate plane, is point R equidistant from points (-3,-3) and (1,-3) ?

Look at the diagram below:

Attachment:

Equidistant points.png [ 9.68 KiB | Viewed 594 times ]

Notice, that the green line (x=-1) is the perpendicular bisector of the line segment with endpoints (-3,-3) and (1,-3), thus ANY point on this line will be equidistant from points (-3,-3) and (1,-3).

(1) The x-coordinate of point R is -1 --> point R is on the green line. Sufficient.
(2) Point R lies on the line y = -3 --> point R may or may not be on the green line. Not sufficient.

Answer: A.
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Re: In the xy-coordinate plane, is point R equidistant from [#permalink]

13 May 2013, 20:17

Walkabout wrote:

In the xy-coordinate plane, is point R equidistant from points (-3,-3) and (1,-3) ?

(1) The x-coordinate of point R is -1.
(2) Point R lies on the line y = -3.

Any point that lie on the perpendicular bisector the line segment with extreme points (-3,-3) and (1,-3) will satisfy this condition. The perpendicular bisector of the line segment is x=-1.

1) this means the point lies on x=-1. Sufficient.
2) This may or may not lie in the middle. The point -1,-3 is the mid point of the line segment but their are other points on the line such as (-2,-3) which doesn't satisfy the requirements. Insufficient.

Hence A.

Re: In the xy-coordinate plane, is point R equidistant from [#permalink] 13 May 2013, 20:17

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In the xy-coordinate plane, is point R equidistant from

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In the xy-coordinate plane, is point R equidistant from

In the xy-coordinate plane, is point R equidistant from

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