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Circle!

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by KICKGMATASS123 » Fri Jul 24, 2009 3:10 pm
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!
OA is B
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by Spaceman Spiff » Fri Jul 24, 2009 3:18 pm
1- The straight line distance between the center (-2, -3) and pt (-2,1) is 4 so the radius of the circle must be > 4 to put that point inside the circle.
2- The straight line distance between the center and pt (4, -3) is 6, so the radius must be <6 for that point to be outside the circle.

1&2 --> 4< radius < 6 --> Answer is B
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by ASS1991 » Fri Jul 24, 2009 3:21 pm
With the coordinates given, it is easy to calculate the distance between the center of the circle and the two points. You don't even have to use the general formula (Root of (Difference of x-values plus Difference of y-values) because in both cases either the x or the y-value remains the same. So the distance of the first point of the center of the circle is 1-(-3)=4, while the other distance is 4-(-2)=6. The only integer between 4 and 6 is 5.
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