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# In the xy-plane, the point (-2, -3) is the center of a circle. The poi

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Joined: 02 Sep 2010
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In the xy-plane, the point (-2, -3) is the center of a circle. The poi  [#permalink]

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18 Nov 2010, 05:25
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76% (01:45) correct 24% (01:55) wrong based on 322 sessions

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

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16 Dec 2015, 23:57
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3
HarveyKlaus wrote:
In the xy-plane the point (-2 -3) is the centre 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 r is an integer then r=

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

In co-ordinate geometry, you should always draw the figure to get the relative placement of points.
Attachment:

Ques3.jpg [ 1.3 MiB | Viewed 7206 times ]

When you draw it, you will see that (-2, 1) is 4 away from the centre and (4, -3) is 6 away from the centre. So the radius of the circle must be between 4 and 6. The only possible value is 5.
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Re: In the xy-plane, the point (-2, -3) is the center of a circle. The poi  [#permalink]

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02 May 2012, 21:13
4
3
(-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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In the xy-plane, the point (-2, -3) is the center of a circle. The poi  [#permalink]

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18 Nov 2010, 05:50
3
1
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

The easiest way to solve this question will be just to mark the points on the coordinate plane. You'll see that the distance between the center (-2, -3) and the point inside the circle (-2, 1) is 4 units (both points are on x=-2 line so the distance will simply be 1-(-3)=4) so the radius must be more than 4, and the distance between the center (-2, -3) and the point outside the circle (4, -3) is 6 units (both points are on y=-3 line so the distance will simply be 4-(-2)=6) so the radius must be less then 6 --> 4<r<6, thus as r is an integer then r=5.

For more on this issues check Coordinate Geometry chapter of Math Book: http://gmatclub.com/forum/math-coordina ... 87652.html

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

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03 May 2012, 00:21
2
2
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 12360 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. The poi  [#permalink]

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12 Mar 2013, 04:47
2
mahendru1992 wrote:
Okay i used another method but i'm not getting the answer
so I used the equation (x-a)^2+(y-b)^2=r^2, and put in the values of the center (-2,-3), which then comes out to be
(x+2)^2+(y+3)^2=r^2. Then i substitute the values of the inside point i.e (-2,1) for x and y and my radius comes out to be 4. I don't know what am i doing wrong here?

What you are doing wrong is that the point (-2,1) doesn't lie ON the circle. You can not substitute this value for the circle's equation.
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Re: In the xy-plane, the point (-2, -3) is the center of a circle. The poi  [#permalink]

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15 Mar 2013, 15:14
2
1
See the attached drawing.

We can easily see by drawing the problem that a Radius=4 is not enough, as the circle will have its frontier in (-2,1) - see the clear circle - and therefore the point will NOT be inside the circle.

If we increase the radius to the next integer Radius=5, this is solved, as the point (-2,1) will fall inside the circle, while the point (4,-3) will fall outside the circle - see the dark circle -. And this is the only feasible solution to the problem.

Solution B
Attachments

Imagen2.jpg [ 10.79 KiB | Viewed 6779 times ]

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

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16 Dec 2015, 16:36
2
HarveyKlaus wrote:
In the xy-plane the point (-2 -3) is the centre 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 r is an integer then r=

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

Can be solved without much calculations.

You are given that (-2,-3) is the center of the circle. Point (4,-3) lies inside the circle ---> the radius is lesser than distance of (-2,-3) from (4,-3) ---> lesser than 6 units but the radius will also be greater than the distance of (-2,-3) from (-2,1) ----> greater than 4 units.

Thus the radius is >4 but <6 and as it is an integer, the only possible value of radius = 5 units.

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

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12 Mar 2013, 03:02
1
Okay i used another method but i'm not getting the answer
so I used the equation (x-a)^2+(y-b)^2=r^2, and put in the values of the center (-2,-3), which then comes out to be
(x+2)^2+(y+3)^2=r^2. Then i substitute the values of the inside point i.e (-2,1) for x and y and my radius comes out to be 4. I don't know what am i doing wrong here?
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Re: In the xy-plane, the point (-2, -3) is the center of a circle. The poi  [#permalink]

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31 Mar 2016, 21:48
1
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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Posts: 8283
Re: In the xy-plane, the point (-2, -3) is the center of a circle. The poi  [#permalink]

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24 Mar 2016, 00:15
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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Re: In the xy-plane, the point (-2, -3) is the center of a circle. The poi  [#permalink]

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18 Jun 2019, 09:35
can anyone explain why it cannot be 4 and has to be > 4?
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Re: In the xy-plane, the point (-2, -3) is the center of a circle. The poi  [#permalink]

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18 Jun 2019, 13:07
hsn81960 wrote:
can anyone explain why it cannot be 4 and has to be > 4?

Certainly!!!!

Radius is the larges distance from the Centre of the Circle to any point on the circumference...

Now, any point within the center doesn't touch the radius , so it can't be the radius and hence we can safely conclude that the radius mst be greater than this figure...

Hope this helps!!!
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Re: In the xy-plane, the point (-2, -3) is the center of a circle. The poi   [#permalink] 18 Jun 2019, 13:07
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