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26 Aug 2025, 10:27
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
25% (00:49) correct
75% (01:40) wrong based on 12 sessions
History
Date
Time
Result
Not Attempted Yet
In the xy-plane, the center of a circle is located at (-8, -11). The point (-8, -8) lies inside the circle, and the point (-11, -7) lies outside the circle. If the circle’s radius is an integer, what is its area?
A. \(4π\)
B. \(9π\)
C. \(16π\)
D. \(25π\)
E. \(36π\)
A. \(4π\)
B. \(9π\)
C. \(16π\)
D. \(25π\)
E. \(36π\)
30 Aug 2025, 07:24
Kudos
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Official Explanation
Make sure to draw the picture. The interior point (-8, -8), is located 3 units directly above the circle’s center (-8, -11), so its distance from the center is 3 units. The exterior point (-11, -7) is located 3 units to the left and 4 units above the circle’s center. Its distance from the center is given by the Pythagorean Theorem as units. If a point 3 units from the center lies inside the circle, while a point 5 units from the center lies outside the circle, then the radius of the circle is between 3 and 5 and must equal 4, since the radius is given as an integer. Then the area, given by \(πr^2,\) equals \(π4^2 = 16π, (C).\)
Answer: C
Make sure to draw the picture. The interior point (-8, -8), is located 3 units directly above the circle’s center (-8, -11), so its distance from the center is 3 units. The exterior point (-11, -7) is located 3 units to the left and 4 units above the circle’s center. Its distance from the center is given by the Pythagorean Theorem as units. If a point 3 units from the center lies inside the circle, while a point 5 units from the center lies outside the circle, then the radius of the circle is between 3 and 5 and must equal 4, since the radius is given as an integer. Then the area, given by \(πr^2,\) equals \(π4^2 = 16π, (C).\)
Answer: C
