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# The vertices of square S have coordinates

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The vertices of square S have coordinates [#permalink]  06 May 2017, 11:35
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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) (1/2, 1/2)
b) (1/2, -1/2)
c) (3/2, 1/2)
d) (3/2, -1/2)
e) (underoot3/2, 1/2)
[Reveal] Spoiler: OA
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Joined: 07 Jun 2014
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GRE 1: Q167 V156
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Re: The vertices of square S have coordinates [#permalink]  07 May 2017, 02:05
Expert's post
HarveyKlaus 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) (1/2, 1/2)
b) (1/2, -1/2)
c) (3/2, 1/2)
d) (3/2, -1/2)
e) (underoot3/2, 1/2)

The easiest way to go about this question is to sketch it and identify which are the diagonally opposite vertices. However there is a shorter way to accomplish the same.

We know that diagonals of a square bisect each other. So in a square ABCD, the coordinates of the point where the diagonals of ABCD intersect.

$$\frac{A + C}{2} = \frac{B + D}{2}$$

or coordinates of the point where the diagonal intersects can be written as = $$\frac{A+B+C+D}{4}$$.

So $$x= \frac{-1 -1 +2 +2}{4}=\frac{1}{2}$$
$$y= \frac{-2 +1 +1 -2}{4}=\frac{-1}{2}$$.

Hence option B is correct!
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Sandy
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Re: The vertices of square S have coordinates   [#permalink] 07 May 2017, 02:05
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