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In the coordinate plane

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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) 3π
(B) 3√2π
(C) 3√3π
(D) 9π
(E) 18π
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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.

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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) = √18
Step 3: Area of circle = pie r^2 = pie * √18 * √18 = 18pie
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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) 3π
(B) 3√2π
(C) 3√3π
(D) 9π
(E) 18π
To find the radius of the circle, you can use the distance formula
Distance = √[(2 - 5)² + (-3 - 0)²]
= √[(-3)² + (-3)²]
= √[9 + 9]
= √18

So, the RADIUS of the circle = √18
Area = πr² = π(√18)² = [spoiler]18π[/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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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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