Find all School-related info fast with the new School-Specific MBA Forum

It is currently 21 Aug 2014, 12:25

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

ABC is a right angle triangle, right angled at B Co ordinate

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
VP
VP
avatar
Status: Final Lap Up!!!
Affiliations: NYK Line
Joined: 21 Sep 2012
Posts: 1096
Location: India
GMAT 1: 410 Q35 V11
GMAT 2: 530 Q44 V20
GMAT 3: 630 Q45 V31
GPA: 3.84
WE: Engineering (Transportation)
Followers: 32

Kudos [?]: 247 [0], given: 67

ABC is a right angle triangle, right angled at B Co ordinate [#permalink] New post 11 Nov 2012, 15:04
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

66% (03:32) correct 34% (02:31) wrong based on 74 sessions
ABC is a right angle triangle, right angled at B Co ordinates of A, B and C are (X,Z), (X,Y) and (X+3, Y) respectively. Length of line AC is 5 units, x and y are greater than or equal to 0, the vertices of triangle ABC have coordinate values as shown, and the value of AC is as shown. If x = 3, then what could be the slope of line AC?

Pls note fig is drawn in 1st quadrant with Z > Y i.e point B is above A.

A. -4/3
B. 2/3
C. 1
D. 4/3
E. 2
[Reveal] Spoiler: OA

Last edited by Archit143 on 11 Nov 2012, 16:35, edited 1 time in total.
Expert Post
Magoosh GMAT Instructor
User avatar
Joined: 28 Dec 2011
Posts: 2025
Followers: 486

Kudos [?]: 1986 [0], given: 30

Re: ABC is a right angle triangle, right angled at B Co ordinate [#permalink] New post 11 Nov 2012, 16:12
Expert's post
Archit143 wrote:
ABC is a right angle triangle, right angled at B Co ordinates of A, B and C are (X,Z), (X,Y) and (X+3, Y) respectively. Length of line AC is 5 units, x and y are greater than or equal to 0, the vertices of triangle ABC have coordinate values as shown, and the value of AC is as shown. If x = 3, then what could be the slope of line AC?
A. -4/3
B. 2/3
C. 1
D. 4/3
E. 2

I'm happy to help with this. :-)

We know the hypotenuse AC = 5, and we know BC = 3, because B & C have the same y-coordinate (BC is horizontal) and they are separated in the horizontal direction by 3.

If a right triangle has a hypotenuse of 5 and one leg of 3, the other leg has to be 4. That is the inescapable conclusion of the Pythagorean Theorem. We must have a 3-4-5 triangle.

The trouble is ---- we don't know if Z > Y or Z < Y ---- the problem provides no information on that point. Thus, we have a horizontal segment BC of length 3, with a right angle at B, but we don't know whether the perpendicular segment AB goes up or down from B. We know AB must have a length of 4 and that it must make a right angle with B, but we don't know whether the direction from B to A is up or down. Therefore, the slope of AB could be either +4/3 or -4/3. Two answers are possible here.

I suspect either something was not copied correctly from the source, or that the source is faulty.

Let me know if you have any questions.

Mike :-)
_________________

Mike McGarry
Magoosh Test Prep

Image

Image

VP
VP
avatar
Status: Final Lap Up!!!
Affiliations: NYK Line
Joined: 21 Sep 2012
Posts: 1096
Location: India
GMAT 1: 410 Q35 V11
GMAT 2: 530 Q44 V20
GMAT 3: 630 Q45 V31
GPA: 3.84
WE: Engineering (Transportation)
Followers: 32

Kudos [?]: 247 [0], given: 67

Re: ABC is a right angle triangle, right angled at B Co ordinate [#permalink] New post 11 Nov 2012, 16:28
mikemcgarry wrote:
Archit143 wrote:
ABC is a right angle triangle, right angled at B Co ordinates of A, B and C are (X,Z), (X,Y) and (X+3, Y) respectively. Length of line AC is 5 units, x and y are greater than or equal to 0, the vertices of triangle ABC have coordinate values as shown, and the value of AC is as shown. If x = 3, then what could be the slope of line AC?
A. -4/3
B. 2/3
C. 1
D. 4/3
E. 2

I'm happy to help with this. :-)

We know the hypotenuse AC = 5, and we know BC = 3, because B & C have the same y-coordinate (BC is horizontal) and they are separated in the horizontal direction by 3.

If a right triangle has a hypotenuse of 5 and one leg of 3, the other leg has to be 4. That is the inescapable conclusion of the Pythagorean Theorem. We must have a 3-4-5 triangle.

The trouble is ---- we don't know if Z > Y or Z < Y ---- the problem provides no information on that point. Thus, we have a horizontal segment BC of length 3, with a right angle at B, but we don't know whether the perpendicular segment AB goes up or down from B. We know AB must have a length of 4 and that it must make a right angle with B, but we don't know whether the direction from B to A is up or down. Therefore, the slope of AB could be either +4/3 or -4/3. Two answers are possible here.

I suspect either something was not copied correctly from the source, or that the source is faulty.

Let me know if you have any questions.

Mike :-)


Hi Mike

First of all thanks for replying to my post.... The actual question is to find the equation of AC which is not difficult after we get the slope.

Pls find below the actual question

In the figure to the left, x and y are greater than or equal to 0, the vertices of triangle ABC have coordinate values as shown, and the value of AC is as shown. If x = 3, then what could be the equation of line AC?

The co ordinates remains the same as in the original question.

My doubt is
When we get the 3 - 4 -5 triangle with clear value as 3 , 4 and 5 not as ratio, also from the equation we know that change in y axis (delta Y ) is 4 and that of X axis is 3. why cant we conclude straight away that the slope is 4/3 .
Yes if we substitute the value of Z as y+ 4 than we get - 4/3

Why is it so..............
The solution assumes the value to be - 4/3 and calculates the equation of line.
Question; why is there two possible SLOPE of a single line.........
VP
VP
avatar
Status: Final Lap Up!!!
Affiliations: NYK Line
Joined: 21 Sep 2012
Posts: 1096
Location: India
GMAT 1: 410 Q35 V11
GMAT 2: 530 Q44 V20
GMAT 3: 630 Q45 V31
GPA: 3.84
WE: Engineering (Transportation)
Followers: 32

Kudos [?]: 247 [0], given: 67

Re: ABC is a right angle triangle, right angled at B Co ordinate [#permalink] New post 11 Nov 2012, 16:34
The line segment AB goes up in the.
The fig is drawn in 1st quadrant and Z > Y
I think that will help to arrive a conclusion

Sorry for the trouble i ll edit the original question.
SVP
SVP
User avatar
Joined: 06 Sep 2013
Posts: 1628
Location: United States
Concentration: Finance
GMAT 1: 710 Q48 V39
WE: Corporate Finance (Investment Banking)
Followers: 11

Kudos [?]: 152 [0], given: 254

GMAT ToolKit User
Re: ABC is a right angle triangle, right angled at B Co ordinate [#permalink] New post 28 Dec 2013, 10:05
Archit143 wrote:
ABC is a right angle triangle, right angled at B Co ordinates of A, B and C are (X,Z), (X,Y) and (X+3, Y) respectively. Length of line AC is 5 units, x and y are greater than or equal to 0, the vertices of triangle ABC have coordinate values as shown, and the value of AC is as shown. If x = 3, then what could be the slope of line AC?

Pls note fig is drawn in 1st quadrant with Z > Y i.e point B is above A.

A. -4/3
B. 2/3
C. 1
D. 4/3
E. 2


A is the answer to this one

Let me explain

We need to draw the triangle first. Now, x =3 so we are going to have a pythagorean triple 3-4-5.
Now are coordinate for A (3,z) C (6,y)

Slope will be (y-z )/ (6-3)

Do we know y-z? Yes we do from the height of the right triangle we get that difference of z-y = 4

Hence y-z will just be -4

So the slope is -4/3

Answer is A

Hope it helps
Cheers!

J :)
1 KUDOS received
Intern
Intern
avatar
Joined: 13 Nov 2013
Posts: 3
Followers: 0

Kudos [?]: 3 [1] , given: 2

Re: ABC is a right angle triangle, right angled at B Co ordinate [#permalink] New post 18 Jan 2014, 12:20
1
This post received
KUDOS
From the option, it is easy to find out the answer.

Right angled triangle == Negative slope. Only one negative option.

So answer A

Method 2:

Since it is coordinate geometry , consider x = 0, y=0.

Then the coordinates A = (0,z) B = (0,0) C = (3,y)

Slope of the equation = (y2-y1)/(x2-x1) and the distance between AC = 5.

So (y-z)^2 = 16 or y-z = + or - 4.

Slope of the hypotenuse is -4/3 or 4/3 . But the hypotenuse will have negative slope, so the answer = -4/3

So the equation will be in the form of 4x+3y+K = 0.
Intern
Intern
avatar
Joined: 06 Jan 2014
Posts: 46
Followers: 0

Kudos [?]: 3 [0], given: 23

GMAT ToolKit User
Re: ABC is a right angle triangle, right angled at B Co ordinate [#permalink] New post 18 Jan 2014, 20:41
mikemcgarry wrote:
Archit143 wrote:
ABC is a right angle triangle, right angled at B Co ordinates of A, B and C are (X,Z), (X,Y) and (X+3, Y) respectively. Length of line AC is 5 units, x and y are greater than or equal to 0, the vertices of triangle ABC have coordinate values as shown, and the value of AC is as shown. If x = 3, then what could be the slope of line AC?
A. -4/3
B. 2/3
C. 1
D. 4/3
E. 2

I'm happy to help with this. :-)

We know the hypotenuse AC = 5, and we know BC = 3, because B & C have the same y-coordinate (BC is horizontal) and they are separated in the horizontal direction by 3.

If a right triangle has a hypotenuse of 5 and one leg of 3, the other leg has to be 4. That is the inescapable conclusion of the Pythagorean Theorem. We must have a 3-4-5 triangle.

The trouble is ---- we don't know if Z > Y or Z < Y ---- the problem provides no information on that point. Thus, we have a horizontal segment BC of length 3, with a right angle at B, but we don't know whether the perpendicular segment AB goes up or down from B. We know AB must have a length of 4 and that it must make a right angle with B, but we don't know whether the direction from B to A is up or down. Therefore, the slope of AB could be either +4/3 or -4/3. Two answers are possible here.

I suspect either something was not copied correctly from the source, or that the source is faulty.

Let me know if you have any questions.

Mike :-)


It is 100% choice D because it is inferable that with the coordinate description (X,Z), (X,Y), (X+3,Y) that X=X and for Y to be parallel, the (X,Z) and (x+3,Y) relationship must be positive
Expert Post
1 KUDOS received
Magoosh GMAT Instructor
User avatar
Joined: 28 Dec 2011
Posts: 2025
Followers: 486

Kudos [?]: 1986 [1] , given: 30

Re: ABC is a right angle triangle, right angled at B Co ordinate [#permalink] New post 19 Jan 2014, 14:18
1
This post received
KUDOS
Expert's post
Archit143 wrote:
ABC is a right angle triangle, right angled at B Co ordinates of A, B and C are (X,Z), (X,Y) and (X+3, Y) respectively. Length of line AC is 5 units, x and y are greater than or equal to 0, the vertices of triangle ABC have coordinate values as shown, and the value of AC is as shown. If x = 3, then what could be the slope of line AC?

Pls note fig is drawn in 1st quadrant with Z > Y i.e point B is above A.

A. -4/3
B. 2/3
C. 1
D. 4/3
E. 2

Apparently Archit added this very important note after I wrote my initial response to the problem. As they say, a picture is worth a thousand words, and a GMAT math problem that includes a diagram often will make little or no sense without the diagram. The GMAT never gives you a diagram unless there's some crucial piece of information you need from the diagram: this is a very important point to appreciate.

With this added piece of information, it's perfectly clear that the answer is (A). If Z > Y, then the line must move DOWN from (X,Z) to (X+3, Y). That's the definition of a negative slope. With the analysis above, we saw that the slope would have to be either -4/3 or +4/3. With the information from the diagram it's clear that the slope is -4/3, answer = (A).

Please let me know if anyone has any further questions.
Mike :-)
_________________

Mike McGarry
Magoosh Test Prep

Image

Image

Manager
Manager
User avatar
Joined: 20 Jul 2012
Posts: 138
Location: India
WE: Information Technology (Computer Software)
Followers: 1

Kudos [?]: 0 [0], given: 241

GMAT ToolKit User CAT Tests
In the figure to the left, x and y are greater than or equal [#permalink] New post 13 Feb 2014, 07:40
In the figure to the left, x and y are greater than or equal to 0, the vertices of triangle ABC have coordinate values as shown, and the value of AC is as shown. If x = 3, then what could be the equation of line AC?
a)4x + 3y = 8
b)3x - 4y = 8
c)4x - 3y = 8
d)4x + 3y = 24
e)3x + 4y = 24
Can someone please help me with this question?My doubt:
[Reveal] Spoiler:
I know it has to be in the form of 4x+3y=something.. But couldn't get how to get the value of c in y=mx+c

Attachments

Capture.PNG
Capture.PNG [ 20.03 KiB | Viewed 631 times ]

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19038
Followers: 3362

Kudos [?]: 24464 [0], given: 2677

Re: In the figure to the left, x and y are greater than or equal [#permalink] New post 13 Feb 2014, 09:29
Expert's post
akankshasoneja wrote:
In the figure to the left, x and y are greater than or equal to 0, the vertices of triangle ABC have coordinate values as shown, and the value of AC is as shown. If x = 3, then what could be the equation of line AC?
a)4x + 3y = 8
b)3x - 4y = 8
c)4x - 3y = 8
d)4x + 3y = 24
e)3x + 4y = 24
Can someone please help me with this question?My doubt:
[Reveal] Spoiler:
I know it has to be in the form of 4x+3y=something.. But couldn't get how to get the value of c in y=mx+c


Merging similar topics. please refer to the solutions above.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Re: In the figure to the left, x and y are greater than or equal   [#permalink] 13 Feb 2014, 09:29
    Similar topics Author Replies Last post
Similar
Topics:
3 Experts publish their posts in the topic Is the triangle ABC, right angled at B? Smita04 5 09 Feb 2012, 17:40
Triangle ABC is right angled at B. BD, the median to soaringAlone 3 04 Jun 2011, 08:08
Is triangle ABC a right triangle? 1. Angle ABC = angle BCA arjtryarjtry 2 28 Aug 2008, 19:23
3 Experts publish their posts in the topic In the diagram to the right, triangle ABC has a right angle abhijit_sen 17 03 Jul 2008, 15:12
Right Angled Triangle vprabhala 1 25 Dec 2004, 20:49
Display posts from previous: Sort by

ABC is a right angle triangle, right angled at B Co ordinate

  Question banks Downloads My Bookmarks Reviews Important topics  


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

Powered by phpBB © phpBB Group and phpBB SEO

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®.