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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  [#permalink]

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04 Jul 2012, 19:19
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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 line y = -3.
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Re: In the xy-coordinate plane, Is point R  [#permalink]

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04 Jul 2012, 20:50
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imhimanshu 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 line y = -3.

Thanks

Hi,

As per below diagram,
Attachment:

xy.jpg [ 11.04 KiB | Viewed 13430 times ]

All the points which lie on x=-1, will be equidistant from the given points,

Using (1),
x coordinate is -1. Sufficient.

Using (2),
point lies on y=-3, the point may lie anywhere on the line joining the two points, and might/might not be equidistant from two given points.
Insufficient.

Regards,
##### General Discussion
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Re: In the xy-coordinate plane, Is point R  [#permalink]

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04 Jul 2012, 21:37
imhimanshu 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 line y = -3.

Thanks

The Answer should be A

1. The x coordinate of point R is -1. Which means that, the point R is (-1, y). Whatever may be the value of 'y', the two points (-3,-3) and (1,-3) will be equidistant to the point (-1,y).

The line x = -1, bisects the line joining, (-3,-3) and (1,-3), hence any point(-1,y) on this line should be of equidistant from the two points

Hence Sufficient.

2. If Point R lies on line y = -3, i.e (x,-3) it means, point R could be anywhere on the line(within the points, outside the points etc) and either way no further evidence is known to identify the value of x in (x,-3).

To be more clear,

if x=-1,Equidistant, --> Yes
if x=0, Not Equidistant, -->No

Hence Not Sufficient.

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

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22 Jul 2014, 16:45
imhimanshu 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 line y = -3.

Thanks

Hi,

As per below diagram,
Attachment:
xy.jpg

All the points which lie on x=-1, will be equidistant from the given points,

Using (1),
x coordinate is -1. Sufficient.

Using (2),
point lies on y=-3, the point may lie anywhere on the line joining the two points, and might/might not be equidistant from two given points.
Insufficient.

Regards,

yes, it is better to draw a diagram to solve the problem.
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Re: In the xy-coordinate plane, is point R equidistant from  [#permalink]

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12 Nov 2015, 19:03
statement 1 is sufficient, because wherever we put point R, it will be equidistant from the both points.
statement 2 is insufficient, since point R can be on -1;-3 which will be a point equidistant from the 2 original ones, or -2;-3 which is not equidistant.
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Re: In the xy-coordinate plane, is point R equidistant from  [#permalink]

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15 Nov 2015, 10:51
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

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 line y = -3.

We get a graph as below:
Attachment:

GCDS inhimanshu In the xy-coordinate plane (20151113).jpg [ 16.17 KiB | Viewed 8293 times ]

In other words, it is asking whether point R is in the same distance from (-3,-3) and (1,-3).
The line x=-1 is in the same distance from the points, so the x-coordinate of R has to be -1. So condition 1 is sufficient,
making the answer A.

Once we modify the original condition and the question according to the variable approach method 1, we can solve approximately 30% of DS questions.
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Re: In the xy-coordinate plane, is point R equidistant from  [#permalink]

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17 Dec 2015, 10:44
First, plot the given points. Any point that is equidistant from the given points needs to be on the line x=-1.

A gives this,
B does not.

A is sufficient

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

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19 Aug 2016, 19:15
Have a query, in statement 1 it is mentioned that x-coordinate is -1, now if I consider 'y' to be -3 or -8 and by applying distance between two points formula, I would get two different values. Shouldn't the y-coordinate value also be known.?
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Re: In the xy-coordinate plane, is point R equidistant from  [#permalink]

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20 Aug 2016, 01:44
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narendran1990 wrote:
Have a query, in statement 1 it is mentioned that x-coordinate is -1, now if I consider 'y' to be -3 or -8 and by applying distance between two points formula, I would get two different values. Shouldn't the y-coordinate value also be known.?

No, the X coordinate value tells us that the point R lines in the line passing through the mid point of the line joining the two given points. Hence, whatever the coordinate of y is, you will get the same distance from the respective points. hence, A is the correct answer.
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In the xy-coordinate plane, is point R equidistant from  [#permalink]

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18 Jan 2018, 10:47
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imhimanshu 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 line y = -3.

Target question: Is point R equidistant from points (-3,-3) and (1,-3)?

This question is a great candidate for rephrasing the target question.
Aside: We have a free video with tips on rephrasing the target question (below)

First sketch the two given points

Notice that the point (-1, -3) is equidistant from the two given points. MORE IMPORTANTLY, every point on the line x = -1 is equidistant from the two given points.

So, we can rephrase the target question . . .
REPHRASED target question: Is point R on the line x = -1?

Statement 1: The x coordinate of point R is -1
If the x-coordinate is -1, then point R is definitely on the line x = -1
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: Point R lies on the line y= -3
This tells us nothing about whether or not point R is on the line x = -1?
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

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

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Re: In the xy-coordinate plane, is point R equidistant from   [#permalink] 09 Mar 2019, 13:08
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