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Coordinate planes aka Geometry

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Coordinate planes aka Geometry

by vinay1983 » Wed Sep 18, 2013 10:18 pm
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. 3pie
B. 3 sqrt 2 pie
C. 3 sqrt 3 pie
D. 9pie
E. 18pie

For this question, there usage of distance formula. Is it really important to know this, GMAT PoV!
Also is there any other method to do this?I have rarely come across this formula in Geometry.

Thanks!
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by theCodeToGMAT » Wed Sep 18, 2013 10:38 pm
Answer is [spoiler][E][/spoiler]
This Question just test your way of interpretation of the actual figure.
By stating that circle centered at (2,-3) and passes (5,0) indicates that
radius = sqrt ( 5-2)^2 + (0+3)^2)) [Distance formula]
= sqrt (18)

Area of circle = (pi) (radius)^2 ==> pi (18)
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by ganeshrkamath » Thu Sep 19, 2013 2:35 am
vinay1983 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. 3pie
B. 3 sqrt 2 pie
C. 3 sqrt 3 pie
D. 9pie
E. 18pie

For this question, there usage of distance formula. Is it really important to know this, GMAT PoV!
Also is there any other method to do this?I have rarely come across this formula in Geometry.

Thanks!
It is an important formula and I think it is within the realm of GMAT.

Radius r of the circle
= distance between the given points
= sqrt((2-5)^2 + (-3-0)^2)
= sqrt(9 + 9)
= sqrt(18)

Area = pi * r^2
= pi * 18

Choose E

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by [email protected] » Thu Sep 19, 2013 12:29 pm
Hi All,

First off, this type of question is absolutely "fair game" for the GMAT.

While the distance formula is one way to solve this problem, you might find drawing a picture to be a bit easier.

1) On a graph, draw a line from (2, -3) to (5,0)
2) Notice this diagonal line is the hypotenuse of a RIGHT TRIANGLE. Draw it.
3) The triangle would have a base = 3 and a height = 3, so the hypotenuse = 3(root2)
4) Radius = 3(root2), so plug into the area formula...

Final Answer: E

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