Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized for You
we will pick new questions that match your level based on your Timer History
Track Your Progress
every week, we’ll send you an estimated GMAT score based on your performance
Practice Pays
we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
Does GMAT RC seem like an uphill battle? e-GMAT is conducting a free webinar to help you learn reading strategies that can enable you to solve 700+ level RC questions with at least 90% accuracy in less than 10 days.
Enter The Economist GMAT Tutor’s Brightest Minds competition – it’s completely free! All you have to do is take our online GMAT simulation test and put your mind to the test. Are you ready? This competition closes on December 13th.
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).
_________________
Regards,
PKN Rise above the storm, you will find the sunshine
Re: In the figure above, ABCD is a square. What are the coordinates of poi
[#permalink]
Show Tags
24 Jul 2018, 11:20
2
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 3427 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)
_________________
SC Butler has resumed! Get two SC questions to practice, whose links you can find by date, here.
Never doubt that a small group of thoughtful, committed citizens can change the world; indeed, it's the only thing that ever has -- Margaret Mead
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.
_________________
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
[#permalink]
Show Tags
16 Aug 2018, 11:05
1
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. _________________
* * * Wish my good luck for 700 before Christmas! If you think my post provided any help, please give +1 kudos, it helps a lot! <3
Re: In the figure above, ABCD is a square. What are the coordinates of poi
[#permalink]
Show Tags
22 Aug 2018, 05:26
1
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 .
Re: In the figure above, ABCD is a square. What are the coordinates of poi
[#permalink]
Show Tags
29 Aug 2019, 22:31
Hello from the GMAT Club BumpBot!
Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
close
74% (02:04) correct 
.
