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GRE Math Challenge#116In the figure above, ABCE is a square [#permalink]
15 May 2015, 11:57
Question Stats:
75% (01:31) correct
25% (02:20) wrong based on 24 sessions
Attachment:
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In the figure above, ABCE is a square. What are the coordinates of point B? (A) (4,2) (B) (2,4) (C) (2,6) (D) (4, 6) (E) (6,2)
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Re: GRE Math Challenge#116In the figure above, ABCE is a square [#permalink]
19 Dec 2017, 10:55
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sandy wrote: In the figure above, ABCE is a square. What are the coordinates of point B? (A) (4,2) (B) (2,4) (C) (2,6) (D) (4, 6) (E) (6,2) Here the distance between the two coordinates (6,0) and (0,4) is given by = \(\sqrt{{(60)^2 + (0+4)^2}}\) =\(\sqrt{52}\) Since the figure is a square all the distance between the each coordinates = \(\sqrt{52}\) Let the coordinate of B = (x,y) Now the distance between the coordinate (6, 0) and (x, y) = \(\sqrt{52}\) or \(\sqrt{{(x+6)^2 + (y0)^2}}\) = \(\sqrt{52}\) Now looking at the values only the above equation satisfy only when x= 2 and y= 6. Hence the coordinate of B is (2,6)
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Re: GRE Math Challenge#116In the figure above, ABCE is a square [#permalink]
19 Dec 2017, 17:13
pranab01 wrote: sandy wrote: In the figure above, ABCE is a square. What are the coordinates of point B? (A) (4,2) (B) (2,4) (C) (2,6) (D) (4, 6) (E) (6,2) Here the distance between the two coordinates (6,0) and (0,4) is given by = \(\sqrt{{(60)^2 + (0+4)^2}}\) =\(\sqrt{52}\) Since the figure is a square all the distance between the each coordinates = \(\sqrt{52}\) Let the coordinate of B = (x,y) Now the distance between the coordinate (6, 0) and (x, y) = \(\sqrt{52}\) or \(\sqrt{{(x+6)^2 + (y0)^2}}\) = \(\sqrt{52}\) Now looking at the values only the above equation satisfy only when x= 2 and y= 6. Hence the coordinate of B is (2,6) Well I can NOT see the pic though



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Re: GRE Math Challenge#116In the figure above, ABCE is a square [#permalink]
20 Dec 2017, 00:36
images are not loading. i have opened in chome and explorer but didnt work out



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Re: GRE Math Challenge#116In the figure above, ABCE is a square [#permalink]
20 Dec 2017, 20:02
Is the diagram visible? and also open up the "spoiler"
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Re: GRE Math Challenge#116In the figure above, ABCE is a square [#permalink]
02 May 2018, 17:52
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Let M be the center of square ABCD. Then, M is the midpoint of both AC and BD. We can find coordinates of M as follows: . M is midpoint of AC > x(M) = (6+4)/2; y(M) = (0+2)/2 or M(1,1) . M is midpoint of BD > x(B) = (2xM  xD) = 20 = 2; y(B) = (2yM  yD) = 2(4) = 6 Finally, we get B(2,6) > C



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Re: GRE Math Challenge#116In the figure above, ABCE is a square [#permalink]
02 Nov 2018, 10:43
Checking options is the best way out



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Re: GRE Math Challenge#116In the figure above, ABCE is a square [#permalink]
08 Jan 2019, 19:37
By visualizing options and coordinates in diagram answer is C.



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Re: GRE Math Challenge#116In the figure above, ABCE is a square [#permalink]
08 Jan 2019, 19:50
grefox wrote: Let M be the center of square ABCD. Then, M is the midpoint of both AC and BD. We can find coordinates of M as follows: . M is midpoint of AC > x(M) = (6+4)/2; y(M) = (0+2)/2 or M(1,1) . M is midpoint of BD > x(B) = (2xM  xD) = 20 = 2; y(B) = (2yM  yD) = 2(4) = 6 Finally, we get B(2,6) > C Different view, and great.



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Re: GRE Math Challenge#116In the figure above, ABCE is a square [#permalink]
24 Jul 2020, 12:44
One more method:
1) We know the line connecting B and D is perpendicular to the line connecting A and C, so the slope of line B>D will be the reciprocal of slope of A>C 2) slope of A>C = (20)/(4+6) = 1/5 3) slope of B>D = negative reciprocal of 1/5, therefore = 5 4) Now for B>D we have y = 5x  4, since coordinates of D are (0, 4) 5) Check answers to see which fits our line. From the figure and the fact that ABCD is a square, we know coordinates of B will be (x, y) where x<0 and y>0, so cross out answer choices D and E 6) In this case, 6 = (5)*(2)  4, so answer is C



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Re: GRE Math Challenge#116In the figure above, ABCE is a square [#permalink]
24 Jul 2020, 20:36
Given Coordinate points: A(6,0) B(x,y) C(4,2) D(0,4) Take Mid points of AC and BD AC: (6+4)/2 and (0+2)/2 AC: (2/2) and (2/2) (x,y) of AC are (1,1) Now take Mid points of BD BD: (x+0)/2 and (y4)/2 BD: x/2 and (y4)/2 Compare with each other: (x,y) of AC are (1,1) and (x,y) of BD are (x/2,(y4)/2) x/2=1 and (y4)/2=1 x=2 and y=6 So coordinates of B are (2,6) Option C
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Re: GRE Math Challenge#116In the figure above, ABCE is a square
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