December 17, 2018 December 17, 2018 06:00 PM PST 07:00 PM PST Join our live webinar and learn how to approach Data Sufficiency and Critical Reasoning problems, how to identify the best way to solve each question and what most people do wrong. December 17, 2018 December 17, 2018 10:00 PM PST 11:00 PM PST From Dec 5th onward, American programs will start releasing R1 decisions. Chat Rooms: We have also assigned chat rooms for every school so that applicants can stay in touch and exchange information/update during decision period.
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 51230

In the figure above, ABCD is a square. What are the coordinates of poi
[#permalink]
Show Tags
03 Jul 2018, 08:15
Question Stats:
77% (02:03) correct 23% (01:54) wrong based on 240 sessions
HideShow timer Statistics




Manager
Joined: 09 Jun 2018
Posts: 185
Location: United States
GPA: 3.95
WE: Manufacturing and Production (Energy and Utilities)

Re: In the figure above, ABCD is a square. What are the coordinates of poi
[#permalink]
Show Tags
03 Jul 2018, 09:48
Another approach: Diagonals will intersect at midpoints of the two lines. Let B be (x,y) So, (x + 0)/2 = (4 + (6))/2 which gives x = 2 (y + (4))/2 = (2+0)/2 which gives y = 6 Hence B is (2,6), Option C.
_________________
If you found this relevant and useful, please Smash that Kudos button!




Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 931
WE: Supply Chain Management (Energy and Utilities)

Re: In the figure above, ABCD is a square. What are the coordinates of poi
[#permalink]
Show Tags
03 Jul 2018, 08:44
Bunuel 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) ABC D is a square as per the given geometrical figure. ("ABC E" may be a typo error) AB  CD Or, slope of line AB=Slope of line CD Or, \(\frac{y0}{x(6)}\)=\(\frac{2(4)}{40}\) (Coordinates 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



Intern
Joined: 04 Apr 2018
Posts: 10
Location: India
GPA: 4

Re: In the figure above, ABCD is a square. What are the coordinates of poi
[#permalink]
Show Tags
24 Jul 2018, 10:20
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.



Senior SC Moderator
Joined: 22 May 2016
Posts: 2218

Re: In the figure above, ABCD is a square. What are the coordinates of poi
[#permalink]
Show Tags
25 Jul 2018, 16:45
Bunuel 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) 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 yaxis, its mirror point would be (4, 2) C's mirror point across the yaxis cannot be a vertex because the square is not symmetric about the axes. • Answer B: (2,4). Distance of B from xaxis MUST be greater than distance of D from xaxis. More than half of the square is in QI and QII. The ycoordinate of B (the height of B from the xaxis) MUST be greater than D's distance from xaxis. D's distance is 4. B must be > 4 That leaves one answer: (2, 6) Answer CAttachment:
square2018.07.25.jpg [ 35.18 KiB  Viewed 1743 times ]
The "box method"If geometric figures are not parallel to the x and yaxes, 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 yaxes. From line segment AO = 6 and properties of a square (parallel sides) we know that one segment of a side of large blueedged square = 6 From line segment DO = 4 and properties of a square we know that the other segment of a blueedged 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 ycoordinate of B is 6. That leaves one answer. (2, 6)Answer CIf you wanted to ascertain the xcoordinate, 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 xcoordinate. Both are 4 away from the yaxis. But segment BY must have length 6 (by property of inscribed square) In QII, then, the distance of B from the yaxis is (64) = 2 Because the vertex is in QII, its xcoordinate is ( 2, 6)



Intern
Joined: 23 Aug 2017
Posts: 26

Re: In the figure above, ABCD is a square. What are the coordinates of poi
[#permalink]
Show Tags
30 Jul 2018, 07:20
Bunuel 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) 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. Option B.



Intern
Joined: 17 May 2018
Posts: 43

Re: In the figure above, ABCD is a square. What are the coordinates of poi
[#permalink]
Show Tags
03 Aug 2018, 07:45
AB and DC are parallel, which means the slopes are identical. Also, distances AB = DC. This means that the change in the xcoordinate and ycoordinate from D to C will be the same as the change from A to B. xcoordinate of D increases by 4 to reach xcoordinate of C ycoordinate of D increases by 6 to reach ycoordinate of C so: xcoordinate of A must increase by 4 to reach xcoordinate of B: 6+4=2 ycoordinate of A must increase by 6 to reach ycoordinate of B: 0+6=6 Therefore the coordinates of B are (2,6). Answer B.
_________________
¿Tienes que presentar el GMAT y no sabes por dónde empezar? ¡Visita GMAT para Principiantes y recibe el curso completo gratis!



Director
Joined: 27 May 2012
Posts: 633

Re: In the figure above, ABCD is a square. What are the coordinates of poi
[#permalink]
Show Tags
11 Aug 2018, 07:00
Bunuel 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) 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.
_________________
 Stne



Math Expert
Joined: 02 Sep 2009
Posts: 51230

Re: In the figure above, ABCD is a square. What are the coordinates of poi
[#permalink]
Show Tags
11 Aug 2018, 13:01
stne wrote: Bunuel 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) 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. _________________ Edited. Thank you.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Director
Joined: 20 Feb 2015
Posts: 795
Concentration: Strategy, General Management

Re: In the figure above, ABCD is a square. What are the coordinates of poi
[#permalink]
Show Tags
12 Aug 2018, 05:24
Bunuel wrote: In the figure above, ABCD 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) 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{(4x)^2+(2y)^2} C satisfies the equation for x and y



Intern
Joined: 28 Mar 2017
Posts: 44
Location: Sweden
Concentration: Finance, Statistics

Re: In the figure above, ABCD is a square. What are the coordinates of poi
[#permalink]
Show Tags
16 Aug 2018, 10:05
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



Intern
Joined: 04 Jul 2018
Posts: 10

Re: In the figure above, ABCD is a square. What are the coordinates of poi
[#permalink]
Show Tags
22 Aug 2018, 04:26
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 &nbs
[#permalink]
22 Aug 2018, 04:26






