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In the figure above, the coordinates of points P and Q are (0, 1) and

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In the figure above, the coordinates of points P and Q are (0, 1) and  [#permalink]

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New post 13 Dec 2017, 21:03
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A
B
C
D
E

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  25% (medium)

Question Stats:

80% (00:32) correct 20% (00:45) wrong based on 33 sessions

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In the figure above, the coordinates of points P and Q are (0, 1) and  [#permalink]

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New post 14 Dec 2017, 12:20
Bunuel wrote:
Image
In the figure above, the coordinates of points P and Q are (0, 1) and (1, 0) respectively. What is the area of square PQRS?

(A) 1
(B) √2
(C) 2
(D) 2√2
(E) 4

Attachment:
2017-12-12_2125_002.png

Let origin be O. Find side length of the square from ∆ OPQ. Its hypotenuse = side of square

∆ OPQ is a right isosceles triangle
Side OP = OQ = 1
∠ at vertex O = 90°
(180° - 90°) = 90° remain
Angles opposite equal sides are equal:
∠ OPQ = ∠ OQP = x : (2x = 90), x = 45°

∆ OPQ has side lengths in ratio \(x : x : x\sqrt{2}\)
x = 1
Hypotenuse* = \(x\sqrt{2}=1\sqrt{2}=\sqrt{2}\)

Area of square = \(s^2=(\sqrt{2})^2= 2\)

Answer C

*OR Pythagorean theorem
\(1^2 + 1^2 = h^2\)
\(2 = h^2\)
\(h = \sqrt{2}\)

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In the figure above, the coordinates of points P and Q are (0, 1) and   [#permalink] 14 Dec 2017, 12:20
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In the figure above, the coordinates of points P and Q are (0, 1) and

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