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) 3√2π
(C) 3√3π
(D) 9Ï€
(E) 18Ï€
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In the coordinate plane
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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
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
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
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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Brent@GMATPrepNow
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To find the radius of the circle, you can use the distance formulashahfahad 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) 3√2π
(C) 3√3π
(D) 9Ï€
(E) 18Ï€
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
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Matt@VeritasPrep
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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.
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.
