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ABCD is a square as per the given geometrical figure. ("ABCE" may be a typo error)
AB || CD Or, slope of line AB=Slope of line CD Or, \(\frac{y-0}{x-(-6)}\)=\(\frac{2-(-4)}{4-0}\) (Co-ordinates of vertex B is (x,y) say) Or,\(y=\frac{3x+18}{2}\)------------(1) Since vertex B lies in \(Q_{2}\), so x<0 & y>0 Option D & E are eliminated. Now, among options A, B, and C; option C satisfies the eq(1) above.
Therefore. Ans(C).
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Re: In the figure above, ABCD is a square. What are the coordinates of poi
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24 Jul 2018, 10:20
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Another Approach:
Since the distance between each of the points, A, B , C and D should be same..So we know that the distance between each of the points should be \sqrt{6^2+4^2}. And only one option (-2,6) gives us that distance.
We can get the answer without calculating anything except two obvious lengths, using either elimination or the "box" method
Eliminate: • Answers D) (4, -6) and E) (6,-2). Coordinates of B are in Q II (-x,y). D and E have (x, -y)
• Answer A: (-4, 2) is the mirror point for C (4, 2). Not allowed. Square is not symmetric about the axes. If you were to flip C across the y-axis, its mirror point would be (-4, 2) C's mirror point across the y-axis cannot be a vertex because the square is not symmetric about the axes.
• Answer B: (-2,4). Distance of B from x-axis MUST be greater than distance of D from x-axis. More than half of the square is in QI and QII. The y-coordinate of B (the height of B from the x-axis) MUST be greater than D's distance from x-axis. D's distance is 4. B must be > 4
That leaves one answer: (-2, 6)
Answer C
Attachment:
square2018.07.25.jpg [ 35.18 KiB | Viewed 1743 times ]
The "box method"
If geometric figures are not parallel to the x- and y-axes, draw a box around the figure.
Now we have congruent right triangles all around the smaller square.
The side lengths of those triangles are easy to find because they are right triangles whose vertical and horizontal legs can be measured with the x- and y-axes.
From line segment AO = 6 and properties of a square (parallel sides) we know that one segment of a side of large blue-edged square = 6
From line segment DO = 4 and properties of a square we know that the other segment of a blue-edged side = 4
A square inscribed in a square divides the sides of the larger square proportionally (Pythagorean theorem)
The larger square's sides are in segments of length 6, 4
Right triangle ABX has height 6. By properties of a right triangle (perpendicular legs), point X and point B are collinear.
The y-coordinate of B is 6. That leaves one answer. (-2, 6)
Answer C
If you wanted to ascertain the x-coordinate, keep in mind the larger square side's a, b, a, b pattern
By properties of a square, Points C and Y MUST have the same x-coordinate. Both are 4 away from the y-axis. But segment BY must have length 6 (by property of inscribed square) In QII, then, the distance of B from the y-axis is (6-4) = 2
Because the vertex is in QII, its x-coordinate is (-2, 6)
We have a right triangle in the third quadrant which sides are 4 and 6, the hypotenuse is 4^2 + 6^2 = \sqrt{52} So, if we would draw a triangle in the forth quadrant the hypotenuse would be \sqrt{52}, the side parallel to the Y axes sould be 6, just option B has this value.
Dear Moderator , There seems to be a small typo here, Square ABCE has come up instead of square ABCD. Hope you will do the needful, Thank you.
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Another one !! since it is a square , the distance between any two points should be same . distance between c and d = \sqrt{42} so \sqrt{42}= \sqrt{(4-x)^2+(2-y)^2} C satisfies the equation for x and y
Re: In the figure above, ABCD is a square. What are the coordinates of poi
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16 Aug 2018, 10:05
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You all give very fine mathematical solutions. Let me give you an alternative that took me 20s. Measure distance from (0,0) to (-6, 0) with my pen. Compare it point B. Seems like x=-2 and Y=6. Check options: Answer is C. PS questions are always drawn to scale unless stated otherwise.
+1 if you think this was useful. _________________
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Re: In the figure above, ABCD is a square. What are the coordinates of poi
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22 Aug 2018, 04:26
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ErikLewe wrote:
You all give very fine mathematical solutions. Let me give you an alternative that took me 20s. Measure distance from (0,0) to (-6, 0) with my pen. Compare it point B. Seems like x=-2 and Y=6. Check options: Answer is C. PS questions are always drawn to scale unless stated otherwise.
+1 if you think this was useful.
That solution should be absolutely fine. I read this approach in the Princeton review book. So it should be approved .
gmatclubot
Re: In the figure above, ABCD is a square. What are the coordinates of poi &nbs
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22 Aug 2018, 04:26
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77% (02:03) correct 
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