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# A circle with center (1, 0) lies in the coordinate plane shown above.

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Math Expert
Joined: 02 Sep 2009
Posts: 52294
A circle with center (1, 0) lies in the coordinate plane shown above.  [#permalink]

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17 Sep 2018, 21:14
00:00

Difficulty:

85% (hard)

Question Stats:

31% (02:34) correct 69% (02:14) wrong based on 29 sessions

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A circle with center (1, 0) lies in the coordinate plane shown above. If points (x, y) and (3, 0) lie on the circle is (x, y) in quadrant 1?

(1) –1 < y < 1
(2) –1 < x < 1

Attachment:

image017.jpg [ 1.42 KiB | Viewed 514 times ]

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examPAL Representative
Joined: 07 Dec 2017
Posts: 868
Re: A circle with center (1, 0) lies in the coordinate plane shown above.  [#permalink]

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18 Sep 2018, 10:53
Bunuel wrote:

A circle with center (1, 0) lies in the coordinate plane shown above. If points (x, y) and (3, 0) lie on the circle is (x, y) in quadrant 1?

(1) –1 < y < 1
(2) –1 < x < 1

Attachment:
image017.jpg

As the circle has center at (1,0) and another point at (3,0), it has radius 2. (because the distance from (3,0) to (1,0) is 2).
In coordinate geometry, making an accurate geometry (an Alternative approach) can help save a lot of work.
In this case, drawing a circle of radius 2 with center at (1,0) we can SEE that the circle passes through all 4 quadrants.

(1) Drawing lines at y = 1 and y = -1 we can SEE that they intersect the circle in all four quadrants. Since we can pick any (x,y) we like between these lines, we can pick any quadrant we like.
Insufficient.
(2) Once again, drawing lines at x = -1 and x = 1, we can SEE the intersections are through the center and tangent to the left edge of the circle. As before, we can pick any points we like.
Insufficient.

Combined. Looking at our drawing, we can see that the only relevant points have x < 0, meaning they are not in the 1st quadrant.
Sufficient.

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Re: A circle with center (1, 0) lies in the coordinate plane shown above. &nbs [#permalink] 18 Sep 2018, 10:53
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