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In an xy-coordinate system, which point lies in the in
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20 Aug 2020, 10:29
20 Aug 2020, 10:29
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In an xy-coordinate system, which point lies in the interior of a circle with center (0,0) and radius 3?
A. (1, −3)
B. (−1, −2)
C. (−3,1)
D. (0,3)
E. (3,3)
A. (1, −3)
B. (−1, −2)
C. (−3,1)
D. (0,3)
E. (3,3)
Re: In an xy-coordinate system, which point lies in the in
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20 Aug 2020, 12:40
20 Aug 2020, 12:40
Attachment:
cricleRad3.PNG [ 4.26 KiB | Viewed 1595 times ]
We'll solve this question by eliminating answer choices.
Notice that in a circle centered at the origin with radius 3, points on the circle with x or y coordinates of 3 are only
(3,0), (0,3), (-3,0), (0,-3)
Any other point with a coordinate of 3 is out of the circle.
Therefore
Option A: (1,-3) (Eliminate. Out of the circle)
Option B: (-1,-2) (Keep)
Option C: (-3, 1) (Eliminate. Out of the circle)
Option D: )0,3) (Eliminate. On the circle)
Option E: (3,3) (Eliminate, Out of the circle)
Final Answer: B
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Re: In an xy-coordinate system, which point lies in the in
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21 Aug 2020, 15:43
21 Aug 2020, 15:43
Carcass wrote:
In an xy-coordinate system, which point lies in the interior of a circle with center (0,0) and radius 3?
A. (1, −3)
B. (−1, −2)
C. (−3,1)
D. (0,3)
E. (3,3)
A. (1, −3)
B. (−1, −2)
C. (−3,1)
D. (0,3)
E. (3,3)
Remind the following properties.
If a point \((x,y)\) is on the circle with a radius \(r\) and a center on the origin, we have \(x^2 + y^ 2 = r^2\).
If a point \((x,y)\) is inside the circle with a radius \(r\) and a center on the origin, we have \(x^2 + y^ 2 < r^2\).
If a point \((x,y)\) is outside the circle with a radius \(r\) and a center on the origin, we have \(x^2 + y^ 2 > r^2\).
A. \((1,-3) : 1^2 + (-3)^2 = 1 + 9 = 10 > 3^2 = 9\). The point is outside the circle.
B. \((-1,-2) : (-1)^2 + (-2)^2 = 1 + 4 = 5 < 3^2 = 9\). The point is inside the circle.
C. \((-3,-1) : (-3)^2 + (-1)^2 = 9 + 1 = 10 > 3^2 = 9\). The point is outside the circle.
D. \((0,3) : 0^2 + 3^2 = 0 + 9 = 3^2 = 9\). The point is on the circle.
E. \((3,3) : 3^2 + 3^2 = 9 + 9 = 18 > 3^2 = 9\). The point is outside the circle.
Therefore, B is the right answer.
