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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:

75% (01:31) correct 25% (02:20) wrong based on 24 sessions
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square.jpg [ 12.91 KiB | Viewed 1628 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
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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

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

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
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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) = -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.
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Re: GRE Math Challenge#116-In 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 = (2-0)/(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#116-In 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 (y-4)/2
BD: x/2 and (y-4)/2

Compare with each other:
(x,y) of AC are (-1,1) and (x,y) of BD are (x/2,(y-4)/2)

x/2=-1 and (y-4)/2=1
x=-2 and y=6

So coordinates of B are (-2,6) Option C
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Re: GRE Math Challenge#116-In the figure above, ABCE is a square   [#permalink] 24 Jul 2020, 20:36
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