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# In the coordinate plane, a circle centered on point (-3, -4) passes th

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Math Expert
Joined: 02 Sep 2009
Posts: 46167
In the coordinate plane, a circle centered on point (-3, -4) passes th [#permalink]

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11 Oct 2015, 09:25
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Difficulty:

25% (medium)

Question Stats:

79% (00:57) correct 21% (00:45) wrong based on 144 sessions

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In the coordinate plane, a circle centered on point (-3, -4) passes through point (1, 1). What is the area of the circle?

A. 9π
B. 18π
C. 25π
D. 37π
E. 41π

Kudos for a correct solution.

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Re: In the coordinate plane, a circle centered on point (-3, -4) passes th [#permalink]

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11 Oct 2015, 10:42
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1
Bunuel wrote:
In the coordinate plane, a circle centered on point (-3, -4) passes through point (1, 1). What is the area of the circle?

A. 9π
B. 18π
C. 25π
D. 37π
E. 41π

Kudos for a correct solution.

We can build a triangle with the given points and find the hypotenuse (Radius) using Pythagorean theorem:
4^2+5^2=r^2 --> 16+25 so the area is equal to 41Pi Answer (E)
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Re: In the coordinate plane, a circle centered on point (-3, -4) passes th [#permalink]

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12 Oct 2015, 10:42
1
Bunuel wrote:
In the coordinate plane, a circle centered on point (-3, -4) passes through point (1, 1). What is the area of the circle?

A. 9π
B. 18π
C. 25π
D. 37π
E. 41π

Kudos for a correct solution.

r^2=(-3-1)^2+(-4-1)^2=16+25=41

Area of circle=πr^2=41π

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Re: In the coordinate plane, a circle centered on point (-3, -4) passes th [#permalink]

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12 Oct 2015, 11:08
1
The circle is with center (-3,-4) and one of the point as (1,1).Using distance equation we can get the radius :
r^2 = sqrt ((-3-1)^2 + (-4-1)^2) or r = 41^1/2

Hence aread = pi (r)^2 = 41 pi
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Re: In the coordinate plane, a circle centered on point (-3, -4) passes th [#permalink]

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12 Oct 2015, 11:26
1
From the distance formula:

r^2= (-3-1)^2 + (-4-1)^2
r^2= 16+25=41

As we know, Area of a Circle=pi * r^2
Therefore, Area of Circle= 41 pi

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Posts: 46167
Re: In the coordinate plane, a circle centered on point (-3, -4) passes th [#permalink]

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18 Oct 2015, 12:04
1
Bunuel wrote:
In the coordinate plane, a circle centered on point (-3, -4) passes through point (1, 1). What is the area of the circle?

A. 9π
B. 18π
C. 25π
D. 37π
E. 41π

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION:

As you know, the area of a circle is $$π(r)^2$$, meaning that your goal is to find the radius of this circle. To go from the center of the circle (-3, -4) to the given point on the circle (1, 1), you move 4 spaces horizontally (from x-coordinate -3 to x-coordinate 1) and 5 spaces vertically (from y-coordinate -4 to y-coordinate 1). That sets up a right triangle in which the hypotenuse is the radius. a^2+b^2=c^2 becomes 4^2+5^2=c^2, so c^2=16+25=41. And here's where a shortcut awaits. Since your job is to take the radius (c in the Pythagorean Theorem) and square it, then multiply by π (π(r)^2) you're actually about done. Since $$r^2=41$$, the answer is $$41π$$.
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Re: In the coordinate plane, a circle centered on point (-3, -4) passes th [#permalink]

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14 Jul 2016, 08:32
Bunuel wrote:
In the coordinate plane, a circle centered on point (-3, -4) passes through point (1, 1). What is the area of the circle?

A. 9π
B. 18π
C. 25π
D. 37π
E. 41π

Kudos for a correct solution.

Apply distance formula between the xy pair of (-3-,4) and (1,1)
The distance so obtained will be the radius of the circle
Once radius is known then $$area = π*r^2$$

$$D= \sqrt{(-3-1)^2+(-4-1)^2}$$
$$D= \sqrt{(-4)^2+(-5)^2}$$

$$D= \sqrt{16+25}$$

$$D= \sqrt{41}$$

$$Radius = \sqrt{41}$$
$$Radius^2 = 41$$

$$Area = Radius^2*π$$

$$Area= 41π$$

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Re: In the coordinate plane, a circle centered on point (-3, -4) passes th [#permalink]

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13 Sep 2017, 10:31
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Re: In the coordinate plane, a circle centered on point (-3, -4) passes th   [#permalink] 13 Sep 2017, 10:31
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