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coordinate plane

by Needgmat » Sun Jul 10, 2016 2:07 am

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

A) 3pie

B) 3 under root 2 pie

C) 3 under root 3 pie

D) 9 pie

E) 18 pie

OAE

Hi Experts ,

I have to do coordinate geometry from the starting. Please advise from where should I do?

Thanks,

Kavin
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by [email protected] » Sun Jul 10, 2016 5:31 am
Hi Needgmat,

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

1) With Geometry/graphing questions, it often helps to draw a quick sketch of whatever the question describes.
2) With the information in this prompt, you'll have a line segment that will equal the radius of the circle in question.
3) Whenever you have a diagonal line segment on a graph, you can draw a right triangle 'around it' (with the diagonal line as the hypotenuse of the right triangle). In that way, you can figure out the length of the line segment.

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by OptimusPrep » Sun Jul 10, 2016 7:55 pm
Needgmat wrote:In the coordinate plane, a circle has a center (2,-3) and passes through the point (5,0). What is the area of the circle?

A) 3pie

B) 3 under root 2 pie

C) 3 under root 3 pie

D) 9 pie

E) 18 pie

OAE

Hi Experts ,

I have to do coordinate geometry from the starting. Please advise from where should I do?

Thanks,

Kavin
Hi Kavin,

For coordinate geometry, you need to understand the basics of the geometry too. That will help you in visualising the diagram.
1. Understand the XY axes
2. Distance between two points
3. Slope of a line
4. Relation between slope of two lines.

There are some of the things that you should be well versed with.

As for the question, since the circle passes through (5,0) the radius will be the line joining the centre (2,-3) and (5,0)
Length of radius = (3^2+3^2)^(1/2) = 18^(1/2)

Area = π*r^2 = π*18

Correct Option: E
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by Jeff@TargetTestPrep » Mon Apr 09, 2018 3:39 pm
Needgmat wrote:In the coordinate plane, a circle has a center (2,-3) and passes through the point (5,0). What is the area of the circle?

A) 3pie

B) 3 under root 2 pie

C) 3 under root 3 pie

D) 9 pie

E) 18 pie
Because the circle passes through point (5,0) and has center (2,-3), we know that the distance between these points is the radius of the circle.

Since we are given the coordinates for each point, the easiest thing to do is to use the distance formula to determine the circle's radius. The distance formula is:

Distance= √[(x2 - x1)^2 + (y2 - y1)^2]

We are given two ordered pairs, so we can label the following:

x1 = 2
x2 = 5

y1 = -3
y2 = 0

When we plug these values into the distance formula, we have:

Distance= √[(5 - 2)^2 + (0 - (-3))^2]

Distance= √[(3)^2 + (3)^2]

Distance= √[9 + 9]

Distance = √[18] = √9 x √2 = 3 x √2

Thus, we know that the radius = 3 x √2.

Finally, we can use the radius to determine the area of the circle.

area = πr^2

area = π(3 x √2)^2 = 18π

Answer: E

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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