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

Question

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

Show Answer

Official Answer

B

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

Bunuel · Accepted Answer

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.

Answer: B.

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

Hope it helps.

Bunuel · Answer

I'd quickly mark the points on a plane to SEE the whole picture: Circle.png 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. Answer: B. 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.

GyanOne · Answer

(-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)

mau5 · Answer

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.

johnwesley · Answer

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: Radius=5

Solution B

ENGRTOMBA2018 · Answer

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.

B is the correct answer.

KarishmaB · Answer

In co-ordinate geometry, you should always draw the figure to get the relative placement of points. Ques3.jpg 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. Answer (B)

chetan2u · Answer

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

OptimusPrepJanielle · Answer

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

hsn81960 · Answer

can anyone explain why it cannot be 4 and has to be > 4?

Abhishek009 · Answer

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!!!

dortinator1234923 · Answer

Hi! Just to be sure; does 'INSIDE the circle' mean that the point cannot be on the line of the circle? Maybe a little far fetched, but as a non-native I wanted to be sure

Thanks 🙏

TargetMBA007 · Answer

Tag Update needed: Source is Gmat-Prep

Bunuel

Bunuel · Answer

_________________________
Updated the tag. Thank you!

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

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