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# The coordinates of the points P, Q, R and S are shown in the figure ab

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Math Expert
Joined: 02 Sep 2009
Posts: 43377
The coordinates of the points P, Q, R and S are shown in the figure ab [#permalink]

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18 Dec 2017, 20:46
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The coordinates of the points P, Q, R and S are shown in the figure above. If PQ and RS are the diagonals of a square, what is the area of the square?

(A) 2√2
(B) 4
(C) 4√2
(D) 8
(E) 8√2

[Reveal] Spoiler:
Attachment:

2017-12-19_0837_002.png [ 10.19 KiB | Viewed 438 times ]
[Reveal] Spoiler: OA

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Re: The coordinates of the points P, Q, R and S are shown in the figure ab [#permalink]

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18 Dec 2017, 20:54
If the figure is a square, diagonals are equal, length of which is 4.

If the length of the diagonal is 4, the length of the side is 4/√2 = 2√2

Area of the square is (2√2)^2 or 8(Option D)

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Posts: 151
The coordinates of the points P, Q, R and S are shown in the figure ab [#permalink]

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19 Dec 2017, 06:32
Bunuel wrote:

The coordinates of the points P, Q, R and S are shown in the figure above. If PQ and RS are the diagonals of a square, what is the area of the square?

(A) 2√2
(B) 4
(C) 4√2
(D) 8
(E) 8√2

[Reveal] Spoiler:
Attachment:
2017-12-19_0837_002.png

Distance between two points: $$\sqrt{(x2-x1)^2+(y2-y1)^2} = \sqrt{(5-1)^2+(5-5)^2}=√16=4$$

Side of square using the diagonal: $$diagonal = side*√2; (4) = side*√2; side = \frac{4}{√2}$$

Area of square: $$side^2=(\frac{4}{√2})^2=\frac{6}{2}=8$$

(D) is the answer.
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Re: The coordinates of the points P, Q, R and S are shown in the figure ab [#permalink]

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15 Jan 2018, 09:27
If the diagonals of a square is a and b, the the area is (a*b)/2
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Re: The coordinates of the points P, Q, R and S are shown in the figure ab [#permalink]

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15 Jan 2018, 19:48
I found the area of each triangle... (1/2 * base * height) * 4 (number of triangles in square)
Re: The coordinates of the points P, Q, R and S are shown in the figure ab   [#permalink] 15 Jan 2018, 19:48
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# The coordinates of the points P, Q, R and S are shown in the figure ab

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