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The vertices of square S have coordinates (-1,- 2), (-1,1), (2,1), an

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Carcass
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The vertices of square S have coordinates (-1,- 2), (-1,1), (2,1), an [#permalink] New post   19 Jul 2021, 07:41
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The vertices of square S have coordinates (-1,-2), (-1,1), (2,1), and (2,-2), respectively. What are the coordinates of the point where the diagonals of S intersect?


A. \((\frac{1}{2},\frac{1}{2})
\)

B. \((\frac{1}{2},-\frac{1}{2})
\)

C. \((\frac{3}{2},\frac{1}{2})\)

D. \((\frac{3}{2},-\frac{1}{2})
\)

E. \((\frac{\sqrt{3}}{2},\frac{1}{2})\)


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Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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Re: The vertices of square S have coordinates (-1,- 2), (-1,1), (2,1), an [#permalink] New post   19 Jul 2021, 10:32
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Carcass wrote:
The vertices of square S have coordinates (-1,-2), (-1,1), (2,1), and (2,-2), respectively. What are the coordinates of the point where the diagonals of S intersect?


A. \((\frac{1}{2},\frac{1}{2})
\)

B. \((\frac{1}{2},-\frac{1}{2})
\)

C. \((\frac{3}{2},\frac{1}{2})\)

D. \((\frac{3}{2},-\frac{1}{2})
\)

E. \((\frac{\sqrt{3}}{2},\frac{1}{2})\)


Remember: The diagonals of a square are equal and perpendicular

Just apply Mid-point formula between the end-points of either diagonal

(-1, 1) and (2, -2)
Mid-point = \(\frac{-1 + 2}{2}, \frac{1 - 2}{2} = \frac{1}{2}, \frac{-1}{2}\)

or (-1, -2) and (2, 1)
Mid-point = \(\frac{-1 + 2}{2}, \frac{-2 + 1}{2} = \frac{1}{2}, \frac{-1}{2}\)

Hence, option B
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Re: The vertices of square S have coordinates (-1,- 2), (-1,1), (2,1), an [#permalink]
19 Jul 2021, 10:32
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