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In the xy-plane, the point with coordinates is the center of
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18 Jan 2016, 16:03
18 Jan 2016, 16:03
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Question Stats:
82% (01:36) correct
17% (02:13) wrong based on 146 sessions
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In the xy-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 ?
\(M=\)
\(M=\)
Practice Questions
Question: 14
Page: 341
Difficulty: medium
Question: 14
Page: 341
Difficulty: medium
Show: :: OA
13
Re: In the xy-plane, the point with coordinates is the center of
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18 Jan 2016, 16:05
18 Jan 2016, 16:05
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Solution
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 \(13.\)
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 \(13.\)
Re: In the xy-plane, the point with coordinates is the center of
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11 Jan 2019, 23:25
11 Jan 2019, 23:25
1
Expert Reply
Carcass wrote:
In the xy-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 ?
\(M=\)
\(M=\)
Practice Questions
Question: 14
Page: 341
Difficulty: medium
Question: 14
Page: 341
Difficulty: medium
Show: :: OA
13
we can see that the coordinates (−6, 5) inside C has x-coord same as centre (-6, -7), thus the difference in y-coord will give us the line of radius... Since (-6, 5) is inside the circle, the radius is GREATER than the difference in y-coord, =>\(r>5-(-7)=12\)
we can also see that the coordinates (8, −7) outside C have y-coord same as centre (-6, -7), thus the difference in x-coord will give us the line of radius... Since (8, −7) is outside the circle, the radius is LESSER than the difference in x-coord, =>\(r<8-(-6)=14\)
Thus \(12<r<14\), and as r is an integer, only 13 fits in
