It is currently 20 Apr 2018, 05:50

Close

GMAT Club Daily Prep

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.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Three of the four vertices of a rectangle in the xy-coordinate plane

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 44573
Three of the four vertices of a rectangle in the xy-coordinate plane [#permalink]

Show Tags

New post 10 Jun 2015, 04:19
Expert's post
8
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

70% (01:38) correct 30% (01:33) wrong based on 286 sessions

HideShow timer Statistics

Three of the four vertices of a rectangle in the xy-coordinate plane are ( –5, 1), ( –4, 4), and (8, 0). What is the fourth vertex?

(A) (–4.5, 2.5)
(B) ( –4, 5)
(C) (6, –2 )
(D) (7, –3 )
(E) (10, 1)

Kudos for a correct solution.
[Reveal] Spoiler: OA

_________________

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?
Extra-hard Quant Tests with Brilliant Analytics

Expert Post
4 KUDOS received
SVP
SVP
User avatar
P
Joined: 08 Jul 2010
Posts: 2066
Location: India
GMAT: INSIGHT
WE: Education (Education)
Reviews Badge
Three of the four vertices of a rectangle in the xy-coordinate plane [#permalink]

Show Tags

New post 10 Jun 2015, 07:51
4
This post received
KUDOS
Expert's post
Bunuel wrote:
Three of the four vertices of a rectangle in the xy-coordinate plane are ( –5, 1), ( –4, 4), and (8, 0). What is the fourth vertex?

(A) (–4.5, 2.5)
(B) ( –4, 5)
(C) (6, –2 )
(D) (7, –3 )
(E) (10, 1)

Kudos for a correct solution.


ALTERNATIVE

Slope of Line joining points A( –5, 1) and B( –4, 4) = (4-1) / [(-4)-(-5)] = 3/1 = m1

Slope of Line joining points B( –4, 4) and C( 8, 0) = (0-4) / [(8)-(-4)] = -4/12 = -1/3 = m2

This also suggests that 4th Point must be in Quadrant IV i.e Option C or D only can be true

i.e. AB and BC lines are perpendicular as m1 * m2 = -1

Slope of Line joining points A(–5, 1) and D( x, y) = (y-1) / (x+5) = m3

Slope of Line joining points C(8, 0) and D( x, y) = (y-0) / (x-8) = m4

Now m3 * m4 = -1

i.e. [(y-1) / (x+5)] * [(y-0) / (x-8)] = -1

i.e \(y(y-1) = -(x+5)*(x-8)\)

Let's Check Option C (6, -2)
LHS = (-2)(-2-1) = 6

RHS = (6+5)(6-8) = -22

INCORRECT

Let's Check Option D (7, -3)
LHS = (-3)(-3-1) = 12

RHS = -(7+5)(7-8) = 12

CORRECT

Answer: Option
[Reveal] Spoiler:
D

_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

Expert Post
3 KUDOS received
SVP
SVP
User avatar
P
Joined: 08 Jul 2010
Posts: 2066
Location: India
GMAT: INSIGHT
WE: Education (Education)
Reviews Badge
Re: Three of the four vertices of a rectangle in the xy-coordinate plane [#permalink]

Show Tags

New post 10 Jun 2015, 07:59
3
This post received
KUDOS
Expert's post
3
This post was
BOOKMARKED
Bunuel wrote:
Three of the four vertices of a rectangle in the xy-coordinate plane are ( –5, 1), ( –4, 4), and (8, 0). What is the fourth vertex?

(A) (–4.5, 2.5)
(B) ( –4, 5)
(C) (6, –2 )
(D) (7, –3 )
(E) (10, 1)

Kudos for a correct solution.


ALTERNATE

Length of Diagonals are same in a Rectangle

i.e. Distance Between ( –5, 1) and (8, 0) should be same as Distance between ( –4, 4) and 4th Vertex (x, y)

i.e. \((0-1)^2+(8+5)^2 = (y-4)^2+(x+4)^2\)

i.e. \(1+169 = (y-4)^2+(x+4)^2\)

Check Options:

4th Vertex can only be in either 1st or 4th Quadrant so Option A and B are already out of sync

Option (C) - (6, –2 ): (y-4)^2+(x+4)^2 = (-6)^2 + (10)^2 = 136 so INCORRECT
(D) (7, –3 ): (y-4)^2+(x+4)^2 = (-7)^2 + (11)^2 = 49+121 = 170 so CORRECT

Answer: Option
[Reveal] Spoiler:
D

_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

Intern
Intern
avatar
Joined: 10 Jun 2013
Posts: 18
Concentration: General Management, Technology
GMAT Date: 06-26-2015
WE: Corporate Finance (Venture Capital)
GMAT ToolKit User
Re: Three of the four vertices of a rectangle in the xy-coordinate plane [#permalink]

Show Tags

New post 13 Jun 2015, 06:43
Draw it on the paper, it takes a few seconds to "guess" the correct answer.

Then we could check the result with the formula for the Distance between two points.

Distance btw (-5;1) and (-4;4) is Sqrt(10)

then the correct point must be distant from (8;0) by Sqrt(10)
3 KUDOS received
Current Student
avatar
Joined: 02 Jun 2015
Posts: 89
Location: Brazil
Concentration: Entrepreneurship, General Management
GPA: 3.3
Re: Three of the four vertices of a rectangle in the xy-coordinate plane [#permalink]

Show Tags

New post 13 Jun 2015, 08:15
3
This post received
KUDOS
Actually this is very easy to be solved if you draw on a paper.

Answer D
Attachments

P_20150613_121052_1.jpg
P_20150613_121052_1.jpg [ 628.24 KiB | Viewed 7227 times ]

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 44573
Re: Three of the four vertices of a rectangle in the xy-coordinate plane [#permalink]

Show Tags

New post 15 Jun 2015, 02:46
Expert's post
2
This post was
BOOKMARKED
Bunuel wrote:
Three of the four vertices of a rectangle in the xy-coordinate plane are ( –5, 1), ( –4, 4), and (8, 0). What is the fourth vertex?

(A) (–4.5, 2.5)
(B) ( –4, 5)
(C) (6, –2 )
(D) (7, –3 )
(E) (10, 1)

Kudos for a correct solution.


MANHATTAN GMAT OFFICIAL SOLUTION:

Your GMAT scratchpad has a grid; use it to plot the diagram to scale.
Attachment:
2015-06-15_1342.png
2015-06-15_1342.png [ 13.23 KiB | Viewed 7167 times ]


“Eyeball” solution: The corner at ( –4, 4) looks like a right angle, so complete the rectangle with the dashed lines shown. The 4th point must be located approximately where the bigger dot is drawn. The closest answer choice is the point (7, –3 ). Alternatively, you could plot all of the answer choice points and see which one “works” with the three given points.

Alternatively, we could solve by checking the slopes of the solid lines we drew between the given points to prove those lines are perpendicular, that is, to prove we have drawn two sides of the rectangle correctly.

The slope of the long solid line = (4- 0)/(-4 - 8) = -1/3.
The slope of the short solid line = (4 - 1)/(-4 - (-5)) = 3.

The product of these slopes is -1/3*3 = -1, proving that the lines are perpendicular.

Compute the location of the 4th point, using the fact that the short sides have the same slope. The known short side connects the points ( –5, 1) and ( –4, 4). In other words, the bottom left corner is 1 to the left and 3 down from the top left corner. The unknown bottom right corner should therefore be 1 to the left and 3 down from the top right corner, or x = 8 – 1 = 7 and y = 0 – 3 = –3, corresponding to the point (7,–3).

The correct answer is D.
_________________

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?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
avatar
Joined: 07 Jun 2015
Posts: 1
Three of the four vertices of a rectangle in the xy-coordinate plane [#permalink]

Show Tags

New post 28 Jun 2015, 12:19
Bunuel wrote:
Bunuel wrote:
Three of the four vertices of a rectangle in the xy-coordinate plane are ( –5, 1), ( –4, 4), and (8, 0). What is the fourth vertex?

(A) (–4.5, 2.5)
(B) ( –4, 5)
(C) (6, –2 )
(D) (7, –3 )
(E) (10, 1)

Kudos for a correct solution.


MANHATTAN GMAT OFFICIAL SOLUTION:

Your GMAT scratchpad has a grid; use it to plot the diagram to scale.
Attachment:
2015-06-15_1342.png


“Eyeball” solution: The corner at ( –4, 4) looks like a right angle, so complete the rectangle with the dashed lines shown. The 4th point must be located approximately where the bigger dot is drawn. The closest answer choice is the point (7, –3 ). Alternatively, you could plot all of the answer choice points and see which one “works” with the three given points.

Alternatively, we could solve by checking the slopes of the solid lines we drew between the given points to prove those lines are perpendicular, that is, to prove we have drawn two sides of the rectangle correctly.

The slope of the long solid line = (4- 0)/(-4 - 8) = -1/3.
The slope of the short solid line = (4 - 1)/(-4 - (-5)) = 3.

The product of these slopes is -1/3*3 = -1, proving that the lines are perpendicular.

Compute the location of the 4th point, using the fact that the short sides have the same slope. The known short side connects the points ( –5, 1) and ( –4, 4). In other words, the bottom left corner is 1 to the left and 3 down from the top left corner. The unknown bottom right corner should therefore be 1 to the left and 3 down from the top right corner, or x = 8 – 1 = 7 and y = 0 – 3 = –3, corresponding to the point (7,–3).

The correct answer is D.



Hi Bunuel, please explain why the rectangle cant be such that one side joins the points (-5,1) and (8,0), and the opposite side joins the points (-4,4) and the unknown? Thats what I did initially, but it led to a wrong answer. What (apparently obvious) clues did I miss? :(

My approach was this: two parallel lines have equal slopes so slope for the line joining (-5,1) and (8,0) = slope for the line joining the points (-4,4) and the unknown. For the latter part (slope involving unknown point), x coordinate would be one unit more than (8,0), since the difference b/w x coordinates is 1 unit here: (-5,1) and (-4,4). Then solved for y (the only unknown variable left now).

TIA!
Expert Post
SVP
SVP
User avatar
P
Joined: 08 Jul 2010
Posts: 2066
Location: India
GMAT: INSIGHT
WE: Education (Education)
Reviews Badge
Three of the four vertices of a rectangle in the xy-coordinate plane [#permalink]

Show Tags

New post 28 Jun 2015, 21:59
mrish7 wrote:
Bunuel wrote:
Bunuel wrote:
Three of the four vertices of a rectangle in the xy-coordinate plane are ( –5, 1), ( –4, 4), and (8, 0). What is the fourth vertex?

(A) (–4.5, 2.5)
(B) ( –4, 5)
(C) (6, –2 )
(D) (7, –3 )
(E) (10, 1)

Kudos for a correct solution.


MANHATTAN GMAT OFFICIAL SOLUTION:

Your GMAT scratchpad has a grid; use it to plot the diagram to scale.
Attachment:
2015-06-15_1342.png


“Eyeball” solution: The corner at ( –4, 4) looks like a right angle, so complete the rectangle with the dashed lines shown. The 4th point must be located approximately where the bigger dot is drawn. The closest answer choice is the point (7, –3 ). Alternatively, you could plot all of the answer choice points and see which one “works” with the three given points.

Alternatively, we could solve by checking the slopes of the solid lines we drew between the given points to prove those lines are perpendicular, that is, to prove we have drawn two sides of the rectangle correctly.

The slope of the long solid line = (4- 0)/(-4 - 8) = -1/3.
The slope of the short solid line = (4 - 1)/(-4 - (-5)) = 3.

The product of these slopes is -1/3*3 = -1, proving that the lines are perpendicular.

Compute the location of the 4th point, using the fact that the short sides have the same slope. The known short side connects the points ( –5, 1) and ( –4, 4). In other words, the bottom left corner is 1 to the left and 3 down from the top left corner. The unknown bottom right corner should therefore be 1 to the left and 3 down from the top right corner, or x = 8 – 1 = 7 and y = 0 – 3 = –3, corresponding to the point (7,–3).

The correct answer is D.



Hi Bunuel, please explain why the rectangle cant be such that one side joins the points (-5,1) and (8,0), and the opposite side joins the points (-4,4) and the unknown? Thats what I did initially, but it led to a wrong answer. What (apparently obvious) clues did I miss? :(

My approach was this: two parallel lines have equal slopes so slope for the line joining (-5,1) and (8,0) = slope for the line joining the points (-4,4) and the unknown. For the latter part (slope involving unknown point), x coordinate would be one unit more than (8,0), since the difference b/w x coordinates is 1 unit here: (-5,1) and (-4,4). Then solved for y (the only unknown variable left now).

TIA!


Hi mrish7,

Considering your argument, the slope of line joining points (-5,1) and (8,0) = -1/13

Now the third point (-4,4) must be joined with (-5, 1) or with (8, 0) to make the other side of rectangle and the new line must have slope of 13 because Product of slopes of two perpendicular lines = -1

Case 1: (-4,4)is joined with (-5, 1), the slope of this line = 3/1

Case 2: (-4,4)is joined with (8, 0) the slope of this line = 4/(-12) = -1/3


Both cases rejected. Therefore this assumption is INCORRECT

I hope it helps!
_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

Manager
Manager
avatar
B
Joined: 22 Feb 2016
Posts: 101
Location: India
Concentration: Economics, Healthcare
GMAT 1: 690 Q42 V47
GMAT 2: 710 Q47 V39
GPA: 3.57
Re: Three of the four vertices of a rectangle in the xy-coordinate plane [#permalink]

Show Tags

New post 15 Oct 2016, 20:09
Isnt there is a formula to do the same?
x coordinate (x1+x3-x2) and y coordinate (y1+y2-y3)??
1 KUDOS received
Manager
Manager
avatar
B
Joined: 22 Feb 2016
Posts: 101
Location: India
Concentration: Economics, Healthcare
GMAT 1: 690 Q42 V47
GMAT 2: 710 Q47 V39
GPA: 3.57
Re: Three of the four vertices of a rectangle in the xy-coordinate plane [#permalink]

Show Tags

New post 15 Oct 2016, 20:14
1
This post received
KUDOS
Just derived - The correct formula is
x coordinate- ( x1+x3-x2) and y coordinate is (y1+y3-y2).
Expert Post
SVP
SVP
User avatar
P
Joined: 08 Jul 2010
Posts: 2066
Location: India
GMAT: INSIGHT
WE: Education (Education)
Reviews Badge
Re: Three of the four vertices of a rectangle in the xy-coordinate plane [#permalink]

Show Tags

New post 15 Oct 2016, 20:49
AmritaSarkar89 wrote:
Just derived - The correct formula is
x coordinate- ( x1+x3-x2) and y coordinate is (y1+y3-y2).


Although your previous score is already pretty decent but if you are considering taking GMAT again to improve it further then a small piece of advice is "Do away with formulas" as much as possible.

A person getting the score as your profile shows can't be illogical and logical people should understand maths logically. It rewards them with greater score always

In Coordinate geometry, ALWAYS DRAW THE FIGURE while solving questions... It makes your understanding very smooth and easy
_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

Manager
Manager
avatar
B
Joined: 22 Feb 2016
Posts: 101
Location: India
Concentration: Economics, Healthcare
GMAT 1: 690 Q42 V47
GMAT 2: 710 Q47 V39
GPA: 3.57
Re: Three of the four vertices of a rectangle in the xy-coordinate plane [#permalink]

Show Tags

New post 15 Oct 2016, 21:18
GMATinsight wrote:
AmritaSarkar89 wrote:
Just derived - The correct formula is
x coordinate- ( x1+x3-x2) and y coordinate is (y1+y3-y2).


Although your previous score is already pretty decent but if you are considering taking GMAT again to improve it further then a small piece of advice is "Do away with formulas" as much as possible.

A person getting the score as your profile shows can't be illogical and logical people should understand maths logically. It rewards them with greater score always

In Coordinate geometry, ALWAYS DRAW THE FIGURE while solving questions... It makes your understanding very smooth and easy



Thanks for your piece of advice.
Yes I am planning on retaking to hit something close to 750. The problem is since our childhood we had been pushed into memorizing formulas and till date I am struggling to get away with that canopy on my thought process.
Honestly yes, I am trying to logically breakdown every problem :)
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 6645
Premium Member
Re: Three of the four vertices of a rectangle in the xy-coordinate plane [#permalink]

Show Tags

New post 07 Apr 2018, 15:20
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Re: Three of the four vertices of a rectangle in the xy-coordinate plane   [#permalink] 07 Apr 2018, 15:20
Display posts from previous: Sort by

Three of the four vertices of a rectangle in the xy-coordinate plane

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.