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

 It is currently 15 Sep 2014, 17:01

### 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

# Finding the vertex of a line using eqn, length, midpoint

Author Message
TAGS:
Intern
Joined: 06 Apr 2011
Posts: 46
Followers: 0

Kudos [?]: 5 [0], given: 4

Finding the vertex of a line using eqn, length, midpoint [#permalink]  12 Dec 2013, 19:23
Hi,
Is it possible to find the vertices of a straight line with the following information?

1) we know the equation of the line
2) we know the length of the line
3) we know the mid-point of the line

For eg: Is it possible to find the end-points of the line?

1) y = \frac{3}{2}x - \frac{1}{2}
2) length = \sqrt{52}
3) mid point of the line is (3,4)
Moderator
Joined: 02 Jul 2012
Posts: 1228
Location: India
Concentration: Strategy
GMAT 1: 740 Q49 V42
GPA: 3.8
WE: Engineering (Energy and Utilities)
Followers: 65

Kudos [?]: 679 [0], given: 116

Re: Finding the vertex of a line using eqn, length, midpoint [#permalink]  12 Dec 2013, 21:10
Thinking graphically, the answer should be yes.

From 1, we can plot the infinite line.
From 3, we can plot the mid point.
From 2, we can plot the end points, which are at a distance of half of the total length from the mid point on either side and are on the infinite line.
_________________

Did you find this post helpful?... Please let me know through the Kudos button.

Thanks To The Almighty - My GMAT Debrief

GMAT Reading Comprehension: 7 Most Common Passage Types

Intern
Joined: 06 Apr 2011
Posts: 46
Followers: 0

Kudos [?]: 5 [0], given: 4

Re: Finding the vertex of a line using eqn, length, midpoint [#permalink]  13 Dec 2013, 05:03
Even graphically, how do we find the respective end points from the mid point each corresponding to a length of \sqrt{52}/2 as with the case of the example in the question?
BSchool Forum Moderator
Status: Hoping to get off the waitlist!
Joined: 09 Sep 2013
Posts: 351
Location: United States
GMAT 1: 740 Q52 V38
Followers: 6

Kudos [?]: 196 [0], given: 126

Re: Finding the vertex of a line using eqn, length, midpoint [#permalink]  13 Dec 2013, 05:33
Sorry, I've edited this as my math was incorrect.

It's possible as MacFauz already pointed out.

Essentially, you want to use the Pythagorean Theorem.
You get x^2 + y^2 = (\sqrt{52}/2)^2.
You can then substitute y (just the slope part!) and get x^2 + (\frac{3}{2}x)^2 = 13.
Solve for this and you get x = 2. Plug this back into y = \frac{3}{2}x and you get y = 3.
So now the two vertices are at (3-2,4-3) and (3+2,4+3).

_________________

My review of some of the CAT practice exams
You can usually find me on gmatclub's chat.

Last edited by farful on 13 Dec 2013, 05:52, edited 1 time in total.
Moderator
Joined: 02 Jul 2012
Posts: 1228
Location: India
Concentration: Strategy
GMAT 1: 740 Q49 V42
GPA: 3.8
WE: Engineering (Energy and Utilities)
Followers: 65

Kudos [?]: 679 [0], given: 116

Re: Finding the vertex of a line using eqn, length, midpoint [#permalink]  13 Dec 2013, 05:41
Thanks for the explanation farful... BTW, I do agree that this might not be a PS question but could very well be a DS question...
_________________

Did you find this post helpful?... Please let me know through the Kudos button.

Thanks To The Almighty - My GMAT Debrief

GMAT Reading Comprehension: 7 Most Common Passage Types

Intern
Joined: 06 Apr 2011
Posts: 46
Followers: 0

Kudos [?]: 5 [0], given: 4

Re: Finding the vertex of a line using eqn, length, midpoint [#permalink]  13 Dec 2013, 06:07
Thanks for explaining. I'm little unclear on why would we substitute just the slope part in the equation and not the intercept?
In this problem, it does work since the y intercept falls beyond one of our end point. Is it always safe to ignore the y intercept?

BTW, I pulled pieces from a PS question to make it sound this way that I thought 'what if this were a DS question'.

farful wrote:
Sorry, I've edited this as my math was incorrect.

It's possible as MacFauz already pointed out.

Essentially, you want to use the Pythagorean Theorem.
You get x^2 + y^2 = (\sqrt{52}/2)^2.
You can then substitute y (just the slope part!) and get x^2 + (\frac{3}{2}x)^2 = 13.
Solve for this and you get x = 2. Plug this back into y = \frac{3}{2}x and you get y = 3.
So now the two vertices are at (3-2,4-3) and (3+2,4+3).

BSchool Forum Moderator
Status: Hoping to get off the waitlist!
Joined: 09 Sep 2013
Posts: 351
Location: United States
GMAT 1: 740 Q52 V38
Followers: 6

Kudos [?]: 196 [0], given: 126

Re: Finding the vertex of a line using eqn, length, midpoint [#permalink]  13 Dec 2013, 12:39
Sorry, I'm not really sure of the best way to explain this.

Let's take an easy example of y = x + 2. From the point (1,3) you want to know the point if you travel \sqrt{2} above the point (1,3). The answer is that you need to move 1 in the x direction, and 1 in the y direction. In fact, it doesn't matter where the intercept is (or the midpoint), if you want to travel \sqrt{2} along a y = x + k line, you will always travel 1 in the x direction and 1 in the y direction.
_________________

My review of some of the CAT practice exams
You can usually find me on gmatclub's chat.

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 4755
Location: Pune, India
Followers: 1112

Kudos [?]: 5022 [1] , given: 164

Re: Finding the vertex of a line using eqn, length, midpoint [#permalink]  16 Dec 2013, 21:14
1
KUDOS
Expert's post
mniyer wrote:
Hi,
Is it possible to find the vertices of a straight line with the following information?

1) we know the equation of the line
2) we know the length of the line
3) we know the mid-point of the line

For eg: Is it possible to find the end-points of the line?

1) y = \frac{3}{2}x - \frac{1}{2}
2) length = \sqrt{52}
3) mid point of the line is (3,4)

You don't have end points of a line. A line extends indefinitely in both directions. You have end points of a line segment.

And yes, you can easily find the end point co-ordinates. But before you do, you need to understand a few things.
The equation of a line is given as y = mx + c
m is the slope of the line. The slope means the change in y coordinate for a unit change in x coordinate. The equation of the line here is y = (3/2)x - 1/2. So for every 1 unit increase in x coordinate, y increases by 1.5 units. Similarly for every 1 unit decrease in x coordinate, y decreases by 1.5 units.

Now, according to the given information, this is what the line segment looks like:
Attachment:

Ques3.jpg [ 11.38 KiB | Viewed 475 times ]

Since the length of the line segment is \sqrt{52}, it must be \sqrt{52}/2 = \sqrt{13} on both sides of the mid point.

Now we need the length of the red arrow and blue arrow to get the coordinates. Since the slope of the line segment is 1.5, it means y coordinate changes by 3 units for every change of 2 units in x coordinate (got rid of the decimal). So length of blue line:length of red line = 3:2
Using pythagorean theorem, (3a)^2 + (2a)^2 = \sqrt{13}^2
a = 1 or -1
So length of blue line is 3 units and length of red line is 2 units.
We obtain the coordinates as (3+2, 4+3) and (3 - 2, 4-3) i.e. (5, 7) and (1, 1)
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options. Veritas Prep Reviews Intern Joined: 06 Apr 2011 Posts: 46 Followers: 0 Kudos [?]: 5 [0], given: 4 Re: Finding the vertex of a line using eqn, length, midpoint [#permalink] 19 Dec 2013, 16:52 **Edited the part highlighted in bold** Great post Karishma! Very insightful. +1 K So going by this method, it appears that we will be able to find the end points of a line segment just by knowing the mid point and [either the length of line segment or the equation of the line]? VeritasPrepKarishma wrote: mniyer wrote: Hi, Is it possible to find the vertices of a straight line with the following information? 1) we know the equation of the line 2) we know the length of the line 3) we know the mid-point of the line For eg: Is it possible to find the end-points of the line? 1) y = \frac{3}{2}x - \frac{1}{2} 2) length = \sqrt{52} 3) mid point of the line is (3,4) You don't have end points of a line. A line extends indefinitely in both directions. You have end points of a line segment. And yes, you can easily find the end point co-ordinates. But before you do, you need to understand a few things. The equation of a line is given as y = mx + c m is the slope of the line. The slope means the change in y coordinate for a unit change in x coordinate. The equation of the line here is y = (3/2)x - 1/2. So for every 1 unit increase in x coordinate, y increases by 1.5 units. Similarly for every 1 unit decrease in x coordinate, y decreases by 1.5 units. Now, according to the given information, this is what the line segment looks like: Attachment: Ques3.jpg Since the length of the line segment is \sqrt{52}, it must be \sqrt{52}/2 = \sqrt{13} on both sides of the mid point. Now we need the length of the red arrow and blue arrow to get the coordinates. Since the slope of the line segment is 1.5, it means y coordinate changes by 3 units for every change of 2 units in x coordinate (got rid of the decimal). So length of blue line:length of red line = 3:2 Using pythagorean theorem, (3a)^2 + (2a)^2 = \sqrt{13}^2 a = 1 or -1 So length of blue line is 3 units and length of red line is 2 units. We obtain the coordinates as (3+2, 4+3) and (3 - 2, 4-3) i.e. (5, 7) and (1, 1) Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 4755 Location: Pune, India Followers: 1112 Kudos [?]: 5022 [0], given: 164 Re: Finding the vertex of a line using eqn, length, midpoint [#permalink] 19 Dec 2013, 17:29 Expert's post mniyer wrote: **Edited the part highlighted in bold** Great post Karishma! Very insightful. +1 K So going by this method, it appears that we will be able to find the end points of a line segment just by knowing the mid point and [either the length of line segment or the equation of the line]? No, along with the mid point, you will need the length of the segment and the slope of the line (given by the equation or separately). Once you have the mid point and the length of the segment, you know you have to go up and down some distance from the mid point but the question is in which direction? You need to know the slop of the line too. I have used the slope of the line which is 3/2 here. It tells us that we move 3 units up for every 2 units right. So this specifies the direction of the line. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Save$100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Intern
Joined: 06 Apr 2011
Posts: 46
Followers: 0

Kudos [?]: 5 [0], given: 4

Re: Finding the vertex of a line using eqn, length, midpoint [#permalink]  19 Dec 2013, 19:50
Yup. Makes sense. Thanks again!
VeritasPrepKarishma wrote:
mniyer wrote:
**Edited the part highlighted in bold**
Great post Karishma! Very insightful. +1 K

So going by this method, it appears that we will be able to find the end points of a line segment just by knowing the mid point and [either the length of line segment or the equation of the line]?

No, along with the mid point, you will need the length of the segment and the slope of the line (given by the equation or separately). Once you have the mid point and the length of the segment, you know you have to go up and down some distance from the mid point but the question is in which direction? You need to know the slop of the line too. I have used the slope of the line which is 3/2 here. It tells us that we move 3 units up for every 2 units right. So this specifies the direction of the line.
Re: Finding the vertex of a line using eqn, length, midpoint   [#permalink] 19 Dec 2013, 19:50
Similar topics Replies Last post
Similar
Topics:
1 If B is the midpoint of AC, what is the length of BE? 6 05 Feb 2012, 18:09
1 If B is the midpoint of AC, what is the length of BE? 3 15 Nov 2010, 11:00
4 Finding length of a line inscribed in a circle (GMATPrep1) 11 18 Sep 2009, 11:54
In xy plane ,does line with eqn y=3x+2 contain the 6 17 Aug 2007, 04:44
In triangle ABC, AB has a length of 10 and D is the midpoint 8 01 Mar 2007, 07:40
Display posts from previous: Sort by