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# If ABCD is a square, what are the coordinates of C?

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If ABCD is a square, what are the coordinates of C? [#permalink]  30 Nov 2018, 18:04
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If ABCD is a square, what are the coordinates of C?

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A. $$(\sqrt{3}, \sqrt{3} )$$

B. $$(\sqrt{3}, 1+ \sqrt{3})$$

C. $$(2 \sqrt{3}, \sqrt{3} )$$

D. $$( 1+ \sqrt{3}, \sqrt{3} )$$

E. $$(\sqrt{3}, 2 \sqrt{3} )$$
[Reveal] Spoiler: OA

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Re: If ABCD is a square, what are the coordinates of C? [#permalink]  06 Dec 2018, 04:31
It's 30-60-90 triangle
The ratio of sides will be 1:\sqrt{3}:2
So if we take origin O
OA=1
OB= \sqrt{3}
Draw a perpendicular from C onto x-axis, and take the intersection point E
Again we have a 30-60-90 triangle where
EC=\sqrt{3}
ED=1
Hence
OE= 1 + \sqrt{3}
EC=\sqrt{3}
Coordinates of C are ( 1+ \sqrt{3} , \sqrt{3} )
It's D
Re: If ABCD is a square, what are the coordinates of C?   [#permalink] 06 Dec 2018, 04:31
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