In the coordinate plane

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shahfahad: Senior | Next Rank: 100 Posts; Posts: 42; Joined: Fri Oct 30, 2015 9:01 am

by shahfahad » Thu Nov 26, 2015 1:47 am

In the coordinate plane, a circle has center (2,-3) and passes through the point (5,0). What is the area of the circle?

(A) 3Ï€
(B) 3âˆš2Ï€
(C) 3âˆš3Ï€
(D) 9Ï€
(E) 18Ï€

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Source: Beat The GMAT — Problem Solving | Thu Nov 26, 2015 1:47 am

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by [email protected] » Thu Nov 26, 2015 11:15 am

Hi shahfahad,

I'm going to give you a couple of hints so that you can re-attempt this question on your own:

1) Draw a graph
2) Place the two co-ordinates into the graph
3) Draw a straight line from one point to the next. THAT line is the RADIUS of the circle.
4) Draw a right triangle 'around' that diagonal line. Using that triangle, you can calculate the radius...and then the area of the circle.

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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shahfahad: Senior | Next Rank: 100 Posts; Posts: 42; Joined: Fri Oct 30, 2015 9:01 am

by shahfahad » Thu Nov 26, 2015 11:54 am

Step 1: Plot both points on the graph and connect the points to the x-axis to form a right angle triangle
Step 2: A right angled triangle is formed with two sides of length 3. The third side can be found using Pythagorean Theorem. 3^2 + 3^2 = x^2. Therefore, x(radius) = âˆš18
Step 3: Area of circle = pie r^2 = pie * âˆš18 * âˆš18 = 18pie

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Thu Nov 26, 2015 12:24 pm

shahfahad wrote:In the coordinate plane, a circle has center (2,-3) and passes through the point (5,0). What is the area of the circle?

(A) 3Ï€
(B) 3âˆš2Ï€
(C) 3âˆš3Ï€
(D) 9Ï€
(E) 18Ï€

To find the radius of the circle, you can use the distance formula
Distance = âˆš[(2 - 5)Â² + (-3 - 0)Â²]
= âˆš[(-3)Â² + (-3)Â²]
= âˆš[9 + 9]
= âˆš18

So, the RADIUS of the circle = âˆš18
Area = Ï€rÂ² = Ï€(âˆš18)Â² = [spoiler]18Ï€[/spoiler]

Answer: E

Here's a free video on finding the distance between two points on the x-y plane: https://www.gmatprepnow.com/module/gmat- ... /video/992

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; GMAT Score:780

by Matt@VeritasPrep » Thu Nov 26, 2015 11:52 pm

Here's a very short approach that games the answer choices.

Since the distance from (2,0) to (5,0) is 3, you know the distance from (2,-3) to (5,0) is greater than 3. Hence the radius > 3, so the area > 9Ï€, and the only possible answer is E.

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