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# GRE Math Challenge#116-In the figure above, ABCE is a square

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GRE Math Challenge#116-In the figure above, ABCE is a square [#permalink]  15 May 2015, 11:57
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Question Stats:

81% (01:46) correct 18% (02:11) wrong based on 11 sessions
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square.jpg [ 12.91 KiB | Viewed 913 times ]

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)
[Reveal] Spoiler: OA

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Re: GRE Math Challenge#116-In the figure above, ABCE is a square [#permalink]  19 Dec 2017, 10:55
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

= $$\sqrt{{(-6-0)^2 + (0+4)^2}}$$ =$$\sqrt{52}$$

Since the figure is a square all the distance between the each coordinates = $$\sqrt{52}$$

Let the co-ordinate of B = (x,y)

Now the distance between the coordinate (-6, 0) and (x, y) = $$\sqrt{52}$$

or $$\sqrt{{(x+6)^2 + (y-0)^2}}$$ = $$\sqrt{52}$$

Now looking at the values only the above equation satisfy only when x= -2 and y= 6.

Hence the co-ordinate of B is (-2,6)
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Re: GRE Math Challenge#116-In 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

= $$\sqrt{{(-6-0)^2 + (0+4)^2}}$$ =$$\sqrt{52}$$

Since the figure is a square all the distance between the each coordinates = $$\sqrt{52}$$

Let the co-ordinate of B = (x,y)

Now the distance between the coordinate (-6, 0) and (x, y) = $$\sqrt{52}$$

or $$\sqrt{{(x+6)^2 + (y-0)^2}}$$ = $$\sqrt{52}$$

Now looking at the values only the above equation satisfy only when x= -2 and y= 6.

Hence the co-ordinate of B is (-2,6)

Well I can NOT see the pic though
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Re: GRE Math Challenge#116-In 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#116-In 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#116-In the figure above, ABCE is a square [#permalink]  02 May 2018, 17:52
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) = -2-0 = -2; y(B) = (2yM - yD) = 2-(-4) = 6
Finally, we get B(-2,6) --> C
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Re: GRE Math Challenge#116-In 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#116-In 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#116-In 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) = -2-0 = -2; y(B) = (2yM - yD) = 2-(-4) = 6
Finally, we get B(-2,6) --> C

Different view, and great.
Re: GRE Math Challenge#116-In the figure above, ABCE is a square   [#permalink] 08 Jan 2019, 19:50
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