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29 Dec 2020, 23:46
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
61% (02:27) correct
39%
(02:27)
wrong
based on 127
sessions
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Not Attempted Yet
The diagonally opposite corners of a square have coordinates of (–1,2) and (5,2) in the standard (x,y) plane. Which of the following represents the coordinates of one of the other corners of the square?
(A) \((5 – 3 \sqrt{2}, \ 2 – 3 \sqrt{2})\)
(B) \((5 – 3 \sqrt{2}, \ 2 + 3 \sqrt{2})\)
(C) (–1, –2)
(D) (1, 2)
(E) (2, –1)
(A) \((5 – 3 \sqrt{2}, \ 2 – 3 \sqrt{2})\)
(B) \((5 – 3 \sqrt{2}, \ 2 + 3 \sqrt{2})\)
(C) (–1, –2)
(D) (1, 2)
(E) (2, –1)
31 Dec 2020, 06:23
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abhinavsodha800
Find the mid-point of the line AB in the above figure.
Let C be the mid-point as mentioned in the above diagram.
\(C(x,y) = (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})\)
\(C(x,y)=(\frac{-1+5}{2},\frac{2+2}{2})=(\frac{4}{2},\frac{4}{2})=(2,2)\)
Distance between \(CD=AC=CB=CE=3\) (From my pervious post)
Now add/subtract \(3\) from the mid-point to get the coordinates of the other diagonals.
\(D(x,y)=(2,2+3)=(2,5)\) Only the y-axis changes and the x-axis remains the same.
\(E(x,y)=(2,2-3)=(2,-1)\) Only the y-axis changes and the x-axis remains the same.
Hope this clarifies. Do let me know if you need any further clarification.
Happy New Year!
General Discussion
30 Dec 2020, 05:13
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Distance between coordinate (–1,2) and (5,2) = \(\sqrt{(5-(-1))^2+(2-2)^2} = \sqrt{6^2}=6\)
The length of the other two sides is \(3\sqrt{2}\) using the Pytheragous theorem.
Below is the image to help with the coordinates.
Ans (E) (2, –1)
The length of the other two sides is \(3\sqrt{2}\) using the Pytheragous theorem.
Below is the image to help with the coordinates.
Ans (E) (2, –1)
Attachments
geogebra-export.png [ 483.1 KiB | Viewed 3166 times ]
