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

 It is currently 25 Apr 2015, 17:20

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Given line L, and a parallel line that runs through point

Author Message
TAGS:
Current Student
Joined: 04 Nov 2012
Posts: 70
Schools: NTU '16 (A)
Followers: 1

Kudos [?]: 33 [1] , given: 39

Given line L, and a parallel line that runs through point [#permalink]  13 Apr 2013, 04:16
1
KUDOS
3
This post was
BOOKMARKED
00:00

Difficulty:

85% (hard)

Question Stats:

55% (03:35) correct 45% (02:15) wrong based on 78 sessions
Attachment:

CG.png [ 47.72 KiB | Viewed 1713 times ]
Given line L (illustrated in graph), and a parallel line that runs through point (-1,5), what is the perimeter of a rectangle whose sides run along the two lines and has a length of 9?

A. 28
B. 9*(15)^0.5
C. 18+2*(20)^0.5
D. 36
E. 45
[Reveal] Spoiler: OA

Last edited by Bunuel on 13 Apr 2013, 04:27, edited 1 time in total.
Renamed the topic and edited the question.
VP
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1125
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
Followers: 139

Kudos [?]: 1343 [2] , given: 219

Re: Given line L, and a parallel line that runs through point [#permalink]  13 Apr 2013, 04:57
2
KUDOS
The parallel line is found using the formula y-y0=m(x-x0) , y-5=3/4(x+1)
The question comes down to what is the distance between $$y=\frac{3}{4}x-\frac{1}{2}$$ and $$y=\frac{3}{4}x+\frac{23}{4}$$?
I was not able to find a quick and easy solution to this question, so I took the perpendicular line $$y=-4/3x$$ and calculated the intersections.
3/4x+23/4=-4/3x point$$(-\frac{69}{25},\frac{92}{25})$$
3/4x-1/2=-4/3x pont$$(\frac{6}{25},-\frac{8}{25})$$
Now using Pitagora we must find the hypotenuse of this triangle which has lengths $$\frac{92+8}{25}=4$$ and $$\frac{69+6}{25}=3$$ (refer to the picture and sorry for the bad quality...)
So hypotenuse = 5 and perimeter = 9+9+5+5=28
Attachments

CG.png [ 58.88 KiB | Viewed 1680 times ]

_________________

It is beyond a doubt that all our knowledge that begins with experience.

Kant , Critique of Pure Reason

Tips and tricks: Inequalities , Mixture | Review: MGMAT workshop
Strategy: SmartGMAT v1.0 | Questions: Verbal challenge SC I-II- CR New SC set out !! , My Quant

Rules for Posting in the Verbal Forum - Rules for Posting in the Quant Forum[/size][/color][/b]

Senior Manager
Joined: 28 Apr 2012
Posts: 308
Location: India
Concentration: Technology, General Management
GMAT 1: 650 Q48 V31
GMAT 2: 770 Q50 V47
WE: Information Technology (Computer Software)
Followers: 17

Kudos [?]: 242 [7] , given: 142

Re: Given line L, and a parallel line that runs through point [#permalink]  13 Apr 2013, 05:36
7
KUDOS
Line:
y = (3/4)x - 1/2

point:
(-1,5)

distance of a point (p,q) from a line ax+by+c = 0 is given by formula:

$$d= |(ap + bq + c)/sqrt(a^2 + b^2)|$$

Simplify the equation:

Multiply 4 in each side:
4y = 3x - 2
=> 3x -4y - 2 = 0

Use the formula:
$$d=|{ 3*(-1) - 4*5 - 2}/ sqrt(3^2 + (-4)^2)| = |(-3 -20 - 2)/5| = |-25/5| = 5$$

Perimeter of the recatangle = 2(length + breadth)
length = 9
breadth = distance of the point from the line = 5

Perimeter = 2*( 9 +5) = 3*14 = 28
Option A.
_________________

"Appreciation is a wonderful thing. It makes what is excellent in others belong to us as well."
― Voltaire

Press Kudos, if I have helped.
Thanks!

shit-happens-my-journey-to-172475.html#p1372807

Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 629
Followers: 54

Kudos [?]: 702 [3] , given: 135

Re: Given line L, and a parallel line that runs through point [#permalink]  15 Apr 2013, 06:19
3
KUDOS
Expert's post
12bhang wrote:
Attachment:
CG.png
Given line L (illustrated in graph), and a parallel line that runs through point (-1,5), what is the perimeter of a rectangle whose sides run along the two lines and has a length of 9?

A. 28
B. 9*(15)^0.5
C. 18+2*(20)^0.5
D. 36
E. 45

The question asks nothing more than calculating the perpendicular distance between the point (-1,5) and the line 3x-4y-2=0. This distance = $$|3(-1)-4(5)-2|/\sqrt{3^2+4^2}$$= |-25|/5 = 5. Thus the perimeter is 2*(5+9) = 28.
A.
_________________
Manager
Joined: 27 Feb 2012
Posts: 138
Followers: 1

Kudos [?]: 24 [0], given: 22

Re: Given line L, and a parallel line that runs through point [#permalink]  15 Apr 2013, 12:12
12bhang wrote:
Attachment:
CG.png
Given line L (illustrated in graph), and a parallel line that runs through point (-1,5), what is the perimeter of a rectangle whose sides run along the two lines and has a length of 9?

A. 28
B. 9*(15)^0.5
C. 18+2*(20)^0.5
D. 36
E. 45

Another way to work out....
The equation of line parallel to y=3/4x-1/2 passing through -1,5 will be
y=3/4x+23/4
Now distance between two parallel lines y=mx+c and y=mx+c1 is given by
= |c1-c| / sq rt(m^2+1)

here we have |23/4 + 1/2| /sq root (3/4^2 + 1) which comes out to be 5.
Perimeter is 9*2 + 5*2 = 28
_________________

---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Please +1 KUDO if my post helps. Thank you.

Intern
Status: Sky is the limit
Affiliations: CIPS
Joined: 01 Apr 2012
Posts: 39
Location: United Arab Emirates
Concentration: General Management, Strategy
GMAT 1: 650 Q49 V31
GMAT 2: 720 Q50 V38
WE: Supply Chain Management (Energy and Utilities)
Followers: 0

Kudos [?]: 19 [0], given: 10

Re: Given line L, and a parallel line that runs through point [#permalink]  27 Apr 2013, 22:01
12bhang wrote:
Attachment:
CG.png
Given line L (illustrated in graph), and a parallel line that runs through point (-1,5), what is the perimeter of a rectangle whose sides run along the two lines and has a length of 9?

A. 28
B. 9*(15)^0.5
C. 18+2*(20)^0.5
D. 36
E. 45

The slope will be same for parallel lines. Hence, we can write the equation of the line which passes through point (-1.5) as y = 3/4x+b.
After substituting the values of x&y, the equation will become,
5=3/4*-1 + b
5 = -3/4 + b
b = 23/4

The question already provides the length of one side and which is equal to 9. Now, we have to find the length of the other side.

In other words, it requires us to find the distance b/w two parallel lines, y = 3/4x - 1/2 & y = 3/4x + 23/4.

The formula to find the distance b/w two parallel lines is |b-c| / √(m²+1)

|23/4 + 1/2| / √(3/4)²+1) = (25/4) / √(25/16) = 5

Hence, the perimeter of the rectangle in the xy plane will become = 2 (9 + 5) = 2*14 = 28
SVP
Joined: 06 Sep 2013
Posts: 2026
Concentration: Finance
GMAT 1: 710 Q48 V39
Followers: 24

Kudos [?]: 290 [0], given: 354

Re: Given line L, and a parallel line that runs through point [#permalink]  14 Apr 2014, 05:17
Here's the way I solved this one.

We basically have a rectangle and we need to find the perimeter 2 (L+W). We know the length is 9, so we need to find the width which is equal to the distance between the two parallel lines

Thus we know that the other line running through (-1,5) is y=3/4x+b

Distance between two parallel lines is 25/4 / sqrt (9/16+1) = 5

Therefore perimeter is thus 28

Hope this helps
Cheers
J
Senior Manager
Joined: 23 Jan 2013
Posts: 281
Schools: Cambridge'16
Followers: 2

Kudos [?]: 42 [0], given: 31

Re: Given line L, and a parallel line that runs through point [#permalink]  14 Apr 2014, 22:48
Slope of perpendicular line to 3/4x-1/2 is equal to -4/3 and this means that we have two legs 4 and 3 and hypotenuse 5 which is side of rectangle, so perimeter is 2*9+2*5=28. Answer is A

Problem is that slope -4/3 can result in hypotenuse equal to 5,10, 15, 20 etc. But only option that fits to answer choices is 5
Re: Given line L, and a parallel line that runs through point   [#permalink] 14 Apr 2014, 22:48
Similar topics Replies Last post
Similar
Topics:
Line m passes through the origin. Line l is parallel to line 5 18 Mar 2012, 20:38
3 If line L passes through 4 31 Mar 2011, 04:45
2 Line L passes through (5,0) and (0,10).If a point is 4 10 Mar 2008, 08:45
Line L passes through point (1,4) and the product of its 9 04 May 2006, 08:30
Line L passes through point (1,4), and the product of its 11 19 Mar 2006, 13:08
Display posts from previous: Sort by