Source: Official Guide for the GMAT 13th Ed. Problem Solving; #69 Official Guide for the GMAT 2015 14th Ed. Problem Solving; #69

4

In the coordinate plane, a circle has

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

2 Explanations

1

A way to avoid drawing could be:

The distance between the center of a circle and a point that lies on the circunference line is the radius.
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A formula to obtain the distance between two points in the coordinate plane:
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Square root of [(x2 - x1)^2 + (y2 - y1)^2] = distance between two points.
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So, we can operate now:
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distance between (5,0) and (2,-3)
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Square root of [(5 - 2)^2 + (0 - -3)^2] =
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Square root of [(3)^2 + (3)^2] =
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Square root of [9 + 9] =
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Square root of [18].
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Let´s simplify the expression:
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Square root of [(3^2) * 2] =
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3 * Square root of [2] = Radius.
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Since the formula of the Area of the circle is:
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pi * r^2
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We can conclude that:
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pi * r^2
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pi * (3 * Square root of [2])^2
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pi * (9 * 2)
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pi * (18)
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Hence, correct answer is 18*pi.

Jan 25, 2015 • Comment

4

Gravatar Mike McGarry, Magoosh Tutor

Dec 27, 2013 • Comment

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Section 5.3 Problem Solving

Section 5.3 Problem Solving

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