It is currently 11 Dec 2017, 14:08

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

The two perpendicular lines L and R intersect at the point

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

Hide Tags

5 KUDOS received
Director
Director
User avatar
Status: Verbal Forum Moderator
Joined: 17 Apr 2013
Posts: 599

Kudos [?]: 649 [5], given: 298

Location: India
GMAT 1: 710 Q50 V36
GMAT 2: 750 Q51 V41
GMAT 3: 790 Q51 V49
GPA: 3.3
The two perpendicular lines L and R intersect at the point [#permalink]

Show Tags

New post 13 Nov 2013, 01:20
5
This post received
KUDOS
7
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

71% (02:14) correct 29% (02:10) wrong based on 221 sessions

HideShow timer Statistics

The two perpendicular lines L and R intersect at the point (3, 4) on the coordinate plane to form a triangle whose other two vertices rest on the x-axis. If one of the other two vertices is located at the origin, what is the x-coordinate of the other vertex?

A. 11/8
B. 33/8
C. 5
D. 20/3
E. 25/3
[Reveal] Spoiler: OA

_________________

Like my post Send me a Kudos :) It is a Good manner.
My Debrief: http://gmatclub.com/forum/how-to-score-750-and-750-i-moved-from-710-to-189016.html

Kudos [?]: 649 [5], given: 298

Expert Post
4 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42544

Kudos [?]: 135259 [4], given: 12679

Re: The two perpendicular lines L and R intersect at the point [#permalink]

Show Tags

New post 13 Nov 2013, 01:56
4
This post received
KUDOS
Expert's post
4
This post was
BOOKMARKED
honchos wrote:
The two perpendicular lines L and R intersect at the point (3, 4) on the coordinate plane to form a triangle whose other two vertices rest on the x-axis. If one of the other two vertices is located at the origin, what is the x-coordinate of the other vertex?

A. 11/8
B. 33/8
C. 5
D. 20/3
E. 25/3


Look at the diagram below:
Attachment:
Untitled.png
Untitled.png [ 6.93 KiB | Viewed 3011 times ]

For a line that crosses two points \((x_1,y_1)\) and \((x_2,y_2)\), slope \(m=\frac{y_2-y_1}{x_2-x_1}\)

Thus the slope of line L passing (0, 0) and (3, 4) is \(m=\frac{y_2-y_1}{x_2-x_1}=\frac{4-0}{3-0}=\frac{4}{3}\).

The slope of line R, which is perpendicular to L, is negative reciprocal of the slope of L, hence its \(-\frac{3}{4}\).

Now, we need to find equation of R.

The equation of a straight line that passes through a point \(P_1(x_1, y_1)\) with a slope m is: \(y-y_1=m(x-x_1)\). Therefore, the equation of R is \(y-4=-\frac{3}{4}(x-3)\) --> \(y=-\frac{3}{4}x+\frac{25}{4}\). The x-intercept of this line is 25/3.

Answer: E.

For more check here: math-coordinate-geometry-87652.html
_________________

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

Kudos [?]: 135259 [4], given: 12679

1 KUDOS received
Senior Manager
Senior Manager
User avatar
S
Joined: 03 Apr 2013
Posts: 289

Kudos [?]: 49 [1], given: 861

GMAT ToolKit User
Re: The two perpendicular lines L and R intersect at the point [#permalink]

Show Tags

New post 16 Nov 2013, 12:55
1
This post received
KUDOS
Hi honchos...you could even do this :-
as bunuel has calculated, the slope of the line will be -3/4. Now suppose the co-ordinates of the point needed are (a,0), just equate the slopes.
You will get the equation
-3/4 = 4/(3-a)
solving this you get the OA 25/3 i.e. E.
Kudos me! :)
_________________

Spread some love..Like = +1 Kudos :)

Kudos [?]: 49 [1], given: 861

Manager
Manager
User avatar
Joined: 10 Jun 2015
Posts: 126

Kudos [?]: 31 [0], given: 0

Re: The two perpendicular lines L and R intersect at the point [#permalink]

Show Tags

New post 22 Aug 2015, 07:07
honchos wrote:
The two perpendicular lines L and R intersect at the point (3, 4) on the coordinate plane to form a triangle whose other two vertices rest on the x-axis. If one of the other two vertices is located at the origin, what is the x-coordinate of the other vertex?

A. 11/8
B. 33/8
C. 5
D. 20/3
E. 25/3


I think this can be solved using similar triangle properties (right angled)
Draw a perpendicular line from the top vertex to x-axis which intersects the axis at (3, 0)
You have one right angled triangle with sides 3, 4, 5
Use the properties to get the other sides.

Kudos [?]: 31 [0], given: 0

Intern
Intern
avatar
B
Joined: 24 Aug 2016
Posts: 1

Kudos [?]: [0], given: 1

Re: The two perpendicular lines L and R intersect at the point [#permalink]

Show Tags

New post 21 Oct 2016, 09:00
Or you can use the distances:
To find the l side you can simply find the distance from (3,4) to (0,0) which is sqr[ (3-0)^2 +(4-0)^2 ] = 5.
The R side is the distance from (3,4) to (x,0) which is : sqr[ (x-3)^2 + (4-0)^2 ]
Finally the other side is sqr[ (x-0)^2 +(0-0)^2 ]=x
Using the property of pythagorean theorem (the triagle is 90 degrees) we find that : x^2=5^2+ {sqr[(x-3)^2 +16]}^2=>
6x=50=>x=25/3. Answer is E

Kudos [?]: [0], given: 1

Director
Director
User avatar
P
Joined: 13 Mar 2017
Posts: 556

Kudos [?]: 139 [0], given: 64

Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: The two perpendicular lines L and R intersect at the point [#permalink]

Show Tags

New post 23 Oct 2017, 23:39
honchos wrote:
The two perpendicular lines L and R intersect at the point (3, 4) on the coordinate plane to form a triangle whose other two vertices rest on the x-axis. If one of the other two vertices is located at the origin, what is the x-coordinate of the other vertex?

A. 11/8
B. 33/8
C. 5
D. 20/3
E. 25/3


Another approach to this problem is
By property of right angled triangle BD^2 = AD * DC
4^2 = 3 * DC
DC = 16/3

AC = AD + DC = 3+16/3 = 25/3

Answer E
Attachments

Triangle.png
Triangle.png [ 7.29 KiB | Viewed 319 times ]


_________________

MBA Social Network : WebMaggu

Appreciate by Clicking +1 Kudos ( Lets be more generous friends.)

Kudos [?]: 139 [0], given: 64

Director
Director
User avatar
P
Joined: 13 Mar 2017
Posts: 556

Kudos [?]: 139 [0], given: 64

Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: The two perpendicular lines L and R intersect at the point [#permalink]

Show Tags

New post 23 Oct 2017, 23:43
honchos wrote:
The two perpendicular lines L and R intersect at the point (3, 4) on the coordinate plane to form a triangle whose other two vertices rest on the x-axis. If one of the other two vertices is located at the origin, what is the x-coordinate of the other vertex?

A. 11/8
B. 33/8
C. 5
D. 20/3
E. 25/3


It can be solved by using slope of a line and slope of perpendicular lines approach:
Slope of AB = 4/3
Slope of AC = -3/4 = (4-0)/(3-x)
-9+3x = 16
x = 25/3
Attachments

Triangle.png
Triangle.png [ 7.29 KiB | Viewed 316 times ]


_________________

MBA Social Network : WebMaggu

Appreciate by Clicking +1 Kudos ( Lets be more generous friends.)

Kudos [?]: 139 [0], given: 64

Re: The two perpendicular lines L and R intersect at the point   [#permalink] 23 Oct 2017, 23:43
Display posts from previous: Sort by

The two perpendicular lines L and R intersect at the point

  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®.