In the xy plane, the point (-2,-3) is the center of a circle : GMAT Problem Solving (PS)
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# In the xy plane, the point (-2,-3) is the center of a circle

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In the xy plane, the point (-2,-3) is the center of a circle [#permalink]

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02 May 2012, 17:55
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In the xy plane, the point (-2,-3) is the center of a circle. The point (-2,1) lies inside the circle and the point (4,-3) lies outside the circle. If the radius r of the circle is an integer, then r=

A. 6
B. 5
C. 4
D. 3
E. 2

Please explain how to approach such questions.
Bunuel: Kindly post a link of similar questions for practice.
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02 May 2012, 20:13
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(-2,-3) is the center of the circle.

(-2,1) lies inside the circle => The radius of the circle is greater than 4 units (as the x coordinates of the center and the point are the same, the distance from the center to the point is the difference in y coordinates, or 4 units)

(4,-3) lies outside the circle => The radius of the circle is less than 6 units

Between 4 and 6, the only integer is 5. Therefore the radius of the circle must be 5 units.

Option (B)
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Re: In the xy plane, the point (-2,-3) is the center of a circle [#permalink]

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02 May 2012, 23:21
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saishankari wrote:
In the xy plane, the point (-2,-3) is the center of a circle. The point (-2,1) lies inside the circle and the point (4,-3) lies outside the circle. If the radius r of the circle is an integer, then r=

A. 6
B. 5
C. 4
D. 3
E. 2

Please explain how to approach such questions.
Bunuel: Kindly post a link of similar questions for practice.

I'd quickly mark the points on a plane to SEE the whole picture:
Attachment:

Circle.png [ 11.45 KiB | Viewed 5861 times ]
You can see that the radius must be more than 4 (since the distance between (-2, -3) and (-2, 1) is 4) but less than 6 (since the distance between (-2,-3) and (4, -3) is 6). It's given that r is an integer therefore r=5.

Theory on Coordinate Geometry: math-coordinate-geometry-87652.html

DS questions on Coordinate Geometry: search.php?search_id=tag&tag_id=41
PS questions on Coordinate Geometry: search.php?search_id=tag&tag_id=62

Hope it helps.
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Re: In the xy plane, the point (-2,-3) is the center of a circle [#permalink]

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23 Dec 2014, 17:02
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In the xy-plane, the point (-2,-3) is the center of a circle. [#permalink]

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23 Mar 2016, 23:07
In the xy-plane, the point (-2,-3) is the center of a circle. The point (-2,1) lies inside the circle and the point (4,-3) lies outside the circle. If the radius r of the circle is an integer, then r =

6
5
4
3
2

Please give a clear solution. Kudos awaits you
Math Expert
Joined: 02 Sep 2009
Posts: 36598
Followers: 7095

Kudos [?]: 93457 [0], given: 10563

Re: In the xy plane, the point (-2,-3) is the center of a circle [#permalink]

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23 Mar 2016, 23:09
Nez wrote:
In the xy-plane, the point (-2,-3) is the center of a circle. The point (-2,1) lies inside the circle and the point (4,-3) lies outside the circle. If the radius r of the circle is an integer, then r =

6
5
4
3
2

Please give a clear solution. Kudos awaits you

Merging topics.

Please search before posting. Thank you.
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Re: In the xy plane, the point (-2,-3) is the center of a circle [#permalink]

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23 Mar 2016, 23:15
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Nez wrote:
In the xy-plane, the point (-2,-3) is the center of a circle. The point (-2,1) lies inside the circle and the point (4,-3) lies outside the circle. If the radius r of the circle is an integer, then r =

6
5
4
3
2

Please give a clear solution. Kudos awaits you

Hi,
lets see the two infos apart from that center is at (-2,-3)..

1)The point (-2,1) lies inside the circle
if you see the similarity in two set of coord X value has not changed but y has changed from 1 to -3..
so distance between these two points= 1(-3)=4
so r>4, as (-2,1) lies inside the circle

2) the point (4,-3) lies outside the circle
here y does not change but only x changes from -2 to 4..
so distance = 4-(-2)=6..
so r<6..

Now r is an integer nad only r as 5 satisfies r>4 and r<6..

B
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Kudos [?]: 393 [1] , given: 21

In the xy plane, the point (-2,-3) is the center of a circle [#permalink]

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31 Mar 2016, 20:48
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Nez wrote:
In the xy-plane, the point (-2,-3) is the center of a circle. The point (-2,1) lies inside the circle and the point (4,-3) lies outside the circle. If the radius r of the circle is an integer, then r =

6
5
4
3
2

Please give a clear solution. Kudos awaits you

This question might look intimidating because of its language, but once you start solving it, you will realise that the options are given to you in such a way that you reach the correct answer easily.

The radius will lie somewhere between the distance of centre from the inner point and the distance from the outer point.

Distance between centre and inner point = Distance between (-2,-3) and (-2, 1)
We can solve for the distance by using the formula for distance between two points. But that is not required here.
If one of the co-ordinates is same, then the distance between two points is simply the difference between the other coordinate.

In this case, Distance = 1 - (-3) = 4

Distance between centre and utter point = Distance between (-2, -3) and (4, -3) = 4 - (-2) = 6

The radius has to be between 4 and 6
On looking at the options, only 5 satisfies
Correct Option: B
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In the xy plane, the point (-2,-3) is the center of a circle   [#permalink] 31 Mar 2016, 20:48
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