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In the xy-plane, the point with coordinates is the center of

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In the xy-plane, the point with coordinates is the center of [#permalink] New post 18 Jan 2016, 16:03
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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 ?

\(M=\)

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Question: 14
Page: 341
Difficulty: medium


[Reveal] Spoiler: OA
13

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Re: In the xy-plane, the point with coordinates is the center of [#permalink] New post 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.

Image

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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Re: In the xy-plane, the point with coordinates is the center of [#permalink] New post 11 Jan 2019, 23:25
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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 ?

\(M=\)

Practice Questions
Question: 14
Page: 341
Difficulty: medium


[Reveal] Spoiler: 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
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Re: In the xy-plane, the point with coordinates is the center of [#permalink] New post 13 Jan 2019, 02:13
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List the points

Center = (-6,-7)
Inside = (-6,5)
Outside= (-8,-7)

use the distance formula for each point's distance from the center.
Start with distance from inside to center, and you'll see that they have the same x coordinate, which means
your x distance is o then you just have to calculate \sqrt{(-7-5)^2}=12
Now do the same thing with distance from outside circle to inside.
they have the same y coordinate of -7, so just calculate the distances of the x coordinate \sqrt{(-6-8)^2} =14

which means the radius has to be the only integer between 12 and 14, which is 13
Re: In the xy-plane, the point with coordinates is the center of   [#permalink] 13 Jan 2019, 02:13
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