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

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Carcass
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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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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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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=

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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
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Re: In the xy-plane, the point with coordinates is the center of [#permalink] New post   09 May 2020, 01:57
Carcass wrote:
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.


Hi Carcass,

You are ignoring the negative signs here while taking difference?
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Re: In the xy-plane, the point with coordinates is the center of [#permalink] New post   09 May 2020, 02:31
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yes.

The question can be solved in seconds based on just your observation

Between the center and the point inside the circle you just need to look at the y coordinate. No need as many people do to use the formula for the distance of two points. Is correct but just a waste of time. A smart GRE student always try to find out a shortcut

(-6,5) and (-6,-7) what you do need is the Y

The distance basically is a vertical line between -7 up to five clearly is the sum. 7+5=12

Same reasoning on the X-axis between (-6,-7) and (8,-7) you need only the x, the horizontal line 8+6=14 but is outside.

You do need a distance between the center AND a point on the circle. So the radius is 13

Maybe if you see this you are able to solve the question in 20 seconds. And it is hard. It is like to see something that is not there. visualization. No need a pencil in this case if not just to make a simple scratch.
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Re: In the xy-plane, the point with coordinates is the center of [#permalink] New post   09 May 2020, 02:52
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Carcass wrote:
yes.

The question can be solved in seconds based on just your observation

Between the center and the point inside the circle you just need to look at the y coordinate. No need as many people do to use the formula for the distance of two points. Is correct but just a waste of time. A smart GRE student always try to find out a shortcut

(-6,5) and (-6,-7) what you do need is the Y

The distance basically is a vertical line between -7 up to five clearly is the sum. 7+5=12

Same reasoning on the X-axis between (-6,-7) and (8,-7) you need only the x, the horizontal line 8+6=14 but is outside.

You do need a distance between the center AND a point on the circle. So the radius is 13

Maybe if you see this you are able to solve the question in 20 seconds. And it is hard. It is like to see something that is not there. visualization. No need a pencil in this case if not just to make a simple scratch.


You made it simple, yes the question is tough. Thanks Carcass :)
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Re: In the xy-plane, the point with coordinates is the center of [#permalink] New post   22 Dec 2024, 02:33
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Re: In the xy-plane, the point with coordinates is the center of [#permalink]
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