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Square ABCD is in the xy-coordinate plane, and each side of the square

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Carcass
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Square ABCD is in the xy-coordinate plane, and each side of the square [#permalink] New post   17 Feb 2021, 05:34
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Square ABCD is in the xy-coordinate plane, and each side of the square is parallel to either the x-axis or the y-axis. Points A and C have coordinates (–2, –1) and (3, 4), respectively.


Quantity A
Quantity B
The area of square ABCD
24



A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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Re: Square ABCD is in the xy-coordinate plane, and each side of the square [#permalink] New post   17 Feb 2021, 07:35
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The coordinates of A & C are given.

ABCD is a square hence AC will be a diagonal of the square.

A(–2, –1) & C(3, 4)

AC = \(\sqrt{(4+1)^2+(3+2)^2}\) = \(\sqrt{50}\)
= 5\(\sqrt{2}\)

In square, the diagonals are \(\sqrt{2}\) times the side of the square.

Hence, side of the square = 5

Qt A

Area = 5*5 = 25

Qt A > Qt B

Answer A
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Re: Square ABCD is in the xy-coordinate plane, and each side of the square [#permalink] New post   17 Feb 2021, 08:12
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Carcass wrote:
Square ABCD is in the xy-coordinate plane, and each side of the square is parallel to either the x-axis or the y-axis. Points A and C have coordinates (–2, –1) and (3, 4), respectively.


Quantity A
Quantity B
The area of square ABCD
24



A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.



Draw a rough Coordinate System, Plot A (-2, -1) and C (3, 4).
AC is the Diagonal of square ABCD.

Distance between 3 and -2 is 5, so the side of the square must be 5
Therefore, Area of Square ABCD = \(5^2 = 25\)

Col. A > Col. B

Hence, A
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Re: Square ABCD is in the xy-coordinate plane, and each side of the square [#permalink]
17 Feb 2021, 08:12
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