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29 Jun 2024, 11:40
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100% (01:51) correct
0% (00:00) wrong based on 2 sessions
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In the x-y plane, the point with coordinates (-6, -7) is the center of circle C. The point with coordinates (-6, 5) lies inside C, and the point with coordinates (8, -7) lies outside C. If m is the radius of C and m is an integer, what is the value of m?
03 Aug 2024, 04:59
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Official Explanation
A strategy that is often helpful in working with geometry problems is drawing a figure that represents the given information as accurately as possible.
In this question you are given that the point with coordinates (-6, -7) is the center of circle C, the point with coordinates (-6, 5) lies inside circle C, and the point with coordinates (8, -7) lies outside circle C, so you could draw the following figure.
From the figure, you can see that the distance between (-6, -7) and (-6, 5) is 7 + 5, or 12, and the radius of C must be greater than 12. You can also see that the distance between (-6, -7) and (8, -7) is 6 + 8, or 14, and the radius of C must be less than 14. Therefore, since the radius is an integer greater than 12 and less than 14, it must be 13.
The correct answer is 13.
A strategy that is often helpful in working with geometry problems is drawing a figure that represents the given information as accurately as possible.
In this question you are given that the point with coordinates (-6, -7) is the center of circle C, the point with coordinates (-6, 5) lies inside circle C, and the point with coordinates (8, -7) lies outside circle C, so you could draw the following figure.
From the figure, you can see that the distance between (-6, -7) and (-6, 5) is 7 + 5, or 12, and the radius of C must be greater than 12. You can also see that the distance between (-6, -7) and (8, -7) is 6 + 8, or 14, and the radius of C must be less than 14. Therefore, since the radius is an integer greater than 12 and less than 14, it must be 13.
The correct answer is 13.
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