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The coordinates of the points P, Q, R and S are shown in the figure ab
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18 Dec 2017, 21:46
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Re: The coordinates of the points P, Q, R and S are shown in the figure ab
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18 Dec 2017, 21:54
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) Posted from my mobile device
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The coordinates of the points P, Q, R and S are shown in the figure ab
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19 Dec 2017, 07:32
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 Attachment: 20171219_0837_002.png Distance between two points: \(\sqrt{(x2x1)^2+(y2y1)^2} = \sqrt{(51)^2+(55)^2}=√16=4\) 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
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15 Jan 2018, 10:27
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
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15 Jan 2018, 20:48
I found the area of each triangle... (1/2 * base * height) * 4 (number of triangles in square)



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Re: The coordinates of the points P, Q, R and S are shown in the figure ab
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23 Feb 2018, 09:57
lets find the distance between SP, or PR, or RQ, or QS
the distance between any of them is √8
so area of the square is 8 = answer choice D
thanks



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The coordinates of the points P, Q, R and S are shown in the figure ab
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23 Feb 2018, 23:41
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 Attachment: 20171219_0837_002.png Three ways to solve, below, are all based on the length of the diagonal. Diagonal = length of line segment RS (or PQ, in which case use xcoordinates instead): \((y_2  y_1) = (7  3) = 4 = d\) 1. Area from diagonal alone: \(A= \frac{d^2}{2}\)Area of square = \(\frac{d^2}{2}=\frac{4^2}{2}=\frac{16}{2}=8\)2. Area from \(s^2\), calculated from diagonal length \(s\sqrt{2} = d\) \(s=\frac{d}{\sqrt{2}}\) \(s=\frac{4}{\sqrt{2}}\) \(Area = s^2\) \(Area = (\frac{4}{\sqrt{2}}*\frac{4}{\sqrt{2}})= \frac{16}{2} = 8\) 3. Area from sides and Pythagorean theorem A square's diagonal is the hypotenuse of an isosceles right triangle. Use Pythagorean theorem: \(s^2 + s^2 = d^2\) \(2s^2 = 4^2\) \(s^2 = \frac{4^2}{2}\) \(Area = s^2 = \frac{4^2}{2}=\frac{16}{2}= 8\) ANSWER D *Note: obvious, but often overlooked. Do not solve for \(s\) in #3. Once you have \(s^2\), you have area.
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Re: The coordinates of the points P, Q, R and S are shown in the figure ab
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12 Mar 2018, 02:35
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 Attachment: 20171219_0837_002.png D1 diagonal one D2=diagonal2 D1=√(51)^2 +(55)^2=4 D2=√(33)^2+(73)^2=4 Area=(D1*D2)/2=(4*4)/2=8



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Re: The coordinates of the points P, Q, R and S are shown in the figure ab
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12 Mar 2018, 03:04
ashisplb wrote: 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 Attachment: 20171219_0837_002.png D1 diagonal one D2=diagonal2 D1=√(51)^2 +(55)^2=4 D2=√(33)^2+(73)^2=4 Area=(D1*D2)/2=(4*4)/2=8Since it is GIVEN to be a square  you don't even need to calculate the length of both the diagonals... since the diagonals of a square are equal in length. Could save a few precious seconds...



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Re: The coordinates of the points P, Q, R and S are shown in the figure ab
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11 Apr 2018, 09:41
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 Attachment: 20171219_0837_002.png Distance between PR = \(\sqrt{(31)^2 + (75)^2}\) PR = \(\sqrt{4 + 4}\) PR = \(2*\sqrt{2}\) Distance between RQ = \(\sqrt{(35)^2 + (75)^2}\) RQ = \(\sqrt{(2)^2 + (2)^2}\) RQ = \(2*\sqrt{2}\) Area of square = PR * RQ \(2\sqrt{2} * 2\sqrt{2}\) Area = 8 Hence (D)
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Re: The coordinates of the points P, Q, R and S are shown in the figure ab &nbs
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