February 21, 2019 February 21, 2019 10:00 PM PST 11:00 PM PST Kick off your 2019 GMAT prep with a free 7day boot camp that includes free online lessons, webinars, and a full GMAT course access. Limited for the first 99 registrants! Feb. 21st until the 27th. February 23, 2019 February 23, 2019 07:00 AM PST 09:00 AM PST Learn reading strategies that can help even nonvoracious reader to master GMAT RC. Saturday, February 23rd at 7 AM PT
Author 
Message 
TAGS:

Hide Tags

Senior Manager
Joined: 21 Jun 2006
Posts: 272

In the xycoordinate system, what is the slope of the line
[#permalink]
Show Tags
Updated on: 19 Jun 2014, 00:16
Question Stats:
74% (02:10) correct 26% (02:34) wrong based on 541 sessions
HideShow timer Statistics
In the xycoordinate system, what is the slope of the line that goes through the origin and is equidistant from the two points P = (1, 11) and Q = (7, 7)? A. 2 B. 2.25 C. 2.50 D. 2.75 E. 3
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by ArvGMAT on 16 Jun 2007, 19:01.
Last edited by Bunuel on 19 Jun 2014, 00:16, edited 1 time in total.
Renamed the topic, edited the question and added the OA.




Manager
Joined: 14 Feb 2011
Posts: 174

Re: co ordinate geometry
[#permalink]
Show Tags
24 Mar 2011, 02:29
AnkitK wrote: what is the slope of the line that goes through the origin and is equidistant from the two points p(1,11) and q(7,7)? A.2 B.2.25 C.2.50 D.2.75 E.3
please provide some tips on co ordinate geometry or some usefull conceptual docs so that i could clear out the concepts of co ordinate geometry. To get a slope of any line, we need at least 2 points that lie on line. We are already given that line passes through origin so one point is \((0,0)\). Also, if p and q are equidistant from the line then the midpoint of line segment connecting P and Q lines on the given lines. Mid point is \(((7+1)/2, (11+7)/2)\) or \((4,9)\). So slope of line is \((90)/(40) = 9/4 = 2.25\). Answer B




Manager
Joined: 23 Dec 2006
Posts: 126

Re: In the xycoordinate system, what is the slope of the line
[#permalink]
Show Tags
16 Jun 2007, 19:09
Use midpoint formula to find point equidistant between P and Q; this point must be a part of our line: ((x1+x2)/2, (y1+y2)/2) = (4,9). Slope = rise/run = 9/4 = 2.25



CEO
Joined: 17 Nov 2007
Posts: 3423
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth)  Class of 2011

Re: PS: Line
[#permalink]
Show Tags
03 Apr 2008, 16:04
Bline: y=ax 1. the line has to pass through the middle point (O) of the segment PQ. 2. the coordinates of the middle point are: (1+(71)/2, 7+(117)/2) = (4,9) 3. 9=a*4 > a=2.25
_________________
HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android)  The OFFICIAL GMAT CLUB PREP APP, a musthave app especially if you aim at 700+  Limited GMAT/GRE Math tutoring in Chicago



Director
Joined: 14 Jan 2007
Posts: 732

Re: PS: Line
[#permalink]
Show Tags
04 Apr 2008, 19:10
walker wrote: B
line: y=ax
1. the line has to pass through the middle point (O) of the segment PQ. 2. the coordinates of the middle point are: (1+(71)/2, 7+(117)/2) = (4,9) 3. 9=a*4 > a=2.25 How can you assume that the line will pass through the mid point of PQ. PQ may not be perpendicular to the line passing through origin.



CEO
Joined: 17 Nov 2007
Posts: 3423
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth)  Class of 2011

Re: PS: Line
[#permalink]
Show Tags
04 Apr 2008, 21:12
PM ┴ y=ax, QN ┴ y=ax PM=QN, QNO=PMO=90° angle POM = angle QON angle OPM = angle OQN So, ∆POM identical with ∆QON and PO=OQ
Attachments
t62132.png [ 2.45 KiB  Viewed 10958 times ]
_________________
HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android)  The OFFICIAL GMAT CLUB PREP APP, a musthave app especially if you aim at 700+  Limited GMAT/GRE Math tutoring in Chicago



Manager
Joined: 11 Feb 2011
Posts: 112

What is the slope of the line that goes through the origin a
[#permalink]
Show Tags
24 Mar 2011, 02:11
What is the slope of the line that goes through the origin and is equidistant from the two points p(1,11) and q(7,7)? A. 2 B. 2.25 C. 2.50 D. 2.75 E. 3
_________________
target:810 out of 800!



Manager
Joined: 11 Feb 2011
Posts: 112

Re: co ordinate geometry
[#permalink]
Show Tags
24 Mar 2011, 02:52
thnkxx beyondgmatscore.Also i was more interested in some theory concepts.
_________________
target:810 out of 800!



Retired Moderator
Joined: 16 Nov 2010
Posts: 1408
Location: United States (IN)
Concentration: Strategy, Technology

Re: co ordinate geometry
[#permalink]
Show Tags
24 Mar 2011, 05:00
@AnkitK, please look here : mathcoordinategeometry87652.html
_________________
Formula of Life > Achievement/Potential = k * Happiness (where k is a constant)
GMAT Club Premium Membership  big benefits and savings



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8891
Location: Pune, India

Re: co ordinate geometry
[#permalink]
Show Tags
24 Mar 2011, 17:32
AnkitK wrote: thnkxx beyondgmatscore.Also i was more interested in some theory concepts. Most coordinate geometry questions become way easier the moment you draw them out... the extra seconds almost always provide a lot of value... Knowing some basic formulas helps and you should be very efficient in drawing lines from their equations, from their slope and a point, from two points etc... Check out the links given below for some concepts on lines, slopes and points.... http://www.veritasprep.com/blog/2010/12 ... hegraphs/http://www.veritasprep.com/blog/2010/12 ... spartii/
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Senior Manager
Joined: 13 Aug 2012
Posts: 420
Concentration: Marketing, Finance
GPA: 3.23

Re: co ordinate geometry
[#permalink]
Show Tags
03 Jan 2013, 04:59
AnkitK wrote: What is the slope of the line that goes through the origin and is equidistant from the two points p(1,11) and q(7,7)? A.2 B.2.25 C.2.50 D.2.75 E.3
First, get the middle coordinate between (1,11) and (7,7)... x = 1 + (71)/2 = 4 y = 7 + (117)/2 = 9 Second, get the slope of (4,9) and (0,0). m = 09 / 04 = 9/4 = 2.25 Answer: B
_________________
Impossible is nothing to God.



Intern
Joined: 23 May 2015
Posts: 5

Re: In the xycoordinate system, what is the slope of the line
[#permalink]
Show Tags
04 Jun 2015, 19:44
Hi All.. I went through the explanation given by walker for vshaunak's query.. I still dont find how are we assuming that those points are on opposite sides of the line...What if both are in the same side of the line?



CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2796
Location: India
GMAT: INSIGHT
WE: Education (Education)

Re: In the xycoordinate system, what is the slope of the line
[#permalink]
Show Tags
05 Jun 2015, 04:36
ragunandan wrote: Hi All.. I went through the explanation given by walker for vshaunak's query.. I still dont find how are we assuming that those points are on opposite sides of the line...What if both are in the same side of the line? Hi Rahghunandan, You are absolutely CORRECT about your doubt. However you need to understand the following two points Case 1) Either a line that is equidistant from the two points must be passing from the the gap between the two points. In this case every point on the line will be equidistant from each of the two given points.OR Case 2) The line that is equidistant must be parallel to the line joining the two points (7, 7) and (1, 11). But this case is applicable only when the perpendicular distance of the Line from point is discussedBut in the case 1) the line will have the positive slope and in case 2) the line will have a negative slope [Slope = (117) / (17) =  (2/3)] and here we have not been given any option of Negative slope. Also the questions doesn't mentioned anything about the perpendicular distance of line from point specifically. Therefore, We will have to consider case 1 only and find the slope of the line that passes through the gap between two lines and is equidistant from two points. I hope it clears your doubt!!!
_________________
Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html
ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION



Intern
Joined: 09 Oct 2015
Posts: 40

Re: In the xycoordinate system, what is the slope of the line
[#permalink]
Show Tags
17 Jul 2016, 05:02
Hi All,
There are two ways 2 points can be equidistant from a line:
Option1: The line passes through the mid point of the two given points.
In this case find the mid point : X coordinate: (1+7)/2 & Y coordinate: (7+11)/2 Coordinates of the mid point: (4,9) Now find the slope of the line between the mid point and the origin: ((90)/(40)) = 2.25
Option 2: The line between the given point P & Q is parallel to a line passing through the origin.
Slope of the line PQ : ((117)/(71)) =4/6 = 2/3 Slope of parallel lines are the same, hence the slope of the line parallel to PQ will also be 2/3
I am not sure if this is an official question or not but my understanding is that if this were to appear in actual GMAT then question will also provide some information that rules out the option of the line being parallel. E.g : The two line do intersect at some point.
Let me know if you found this useful!
Regards, Shradha



Manager
Joined: 17 Jun 2015
Posts: 206
GMAT 1: 540 Q39 V26 GMAT 2: 680 Q46 V37

Re: In the xycoordinate system, what is the slope of the line
[#permalink]
Show Tags
08 Sep 2016, 16:30
sgrover18 wrote: Hi All,
There are two ways 2 points can be equidistant from a line:
Option1: The line passes through the mid point of the two given points.
In this case find the mid point : X coordinate: (1+7)/2 & Y coordinate: (7+11)/2 Coordinates of the mid point: (4,9) Now find the slope of the line between the mid point and the origin: ((90)/(40)) = 2.25
Option 2: The line between the given point P & Q is parallel to a line passing through the origin.
Slope of the line PQ : ((117)/(71)) =4/6 = 2/3 Slope of parallel lines are the same, hence the slope of the line parallel to PQ will also be 2/3
I am not sure if this is an official question or not but my understanding is that if this were to appear in actual GMAT then question will also provide some information that rules out the option of the line being parallel. E.g : The two line do intersect at some point.
Let me know if you found this useful!
Regards, Shradha Indeed, this seems to be a fair point that you've pointed out. However, I guess the slope for the parallel line would be (2/3).
_________________
Fais de ta vie un rêve et d'un rêve une réalité



Director
Joined: 12 Nov 2016
Posts: 725
Location: United States
GPA: 2.66

Re: In the xycoordinate system, what is the slope of the line
[#permalink]
Show Tags
14 Jun 2017, 21:48
ArvGMAT wrote: In the xycoordinate system, what is the slope of the line that goes through the origin and is equidistant from the two points P = (1, 11) and Q = (7, 7)?
A. 2 B. 2.25 C. 2.50 D. 2.75 E. 3 This question is certainly much easier if you have a solid board with a plane on it https://www.amazon.com/ManhattanGMATS ... %2F+MarkerAnyways, if we draw out points P and Q on a plane and create a triangle (this step is not really necessary but may help certain test takers) then we can see that height of the triangle is 4 and the length 6. Let our imaginary point be "K" the x coordinate for this point would exist halfway on the length of the triangle so since our length is 6 half of the length is 3 and 3 spots from the x value of point P, "1" would be 4. The same holds true for the Y value the y value of our point "K" exists halfway on the length of the triangle another to think of it is what is the median of the values 7 8 9 10 11 on this logic the y value is 9. Finally, when the question says that the imaginary line passes through the original this simply means that there is no y intercept for the line's equation in other words any equation of the line would not have the plus or minus part ( example: y= 4x +2 this has a y intercept; y= 5x 2  this has a y intercept). Knowing this you can simply translate the individual answer choices into equations and solve until you find an equation that satisfies the coordinates (4,9) for example Choice E y= 3x 9= 3(4) 9 does not equal 3(4) Choice B 9= 2.25x 9= 2 (1/4)x 9= 2(1/4) 4 9= (9/4) 4 9= 36/4 Therefore "B"



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2827

Re: In the xycoordinate system, what is the slope of the line
[#permalink]
Show Tags
06 Jul 2017, 16:30
ArvGMAT wrote: In the xycoordinate system, what is the slope of the line that goes through the origin and is equidistant from the two points P = (1, 11) and Q = (7, 7)?
A. 2 B. 2.25 C. 2.50 D. 2.75 E. 3 Since the line is equidistant from P = (1, 11) and Q = (7, 7), it must pass through the midpoint between P = (1, 11) and Q = (7, 7). We can use the midpoint formula: Midpoint = ((x1 + x2)/2, (y1 + y2)/2) Midpoint = ((1 + 7)/2, (11 + 7)/2) Midpoint = (4, 9) Since the line also passes through the origin, (0, 0), the slope is: Slope = change in y/change in x (9  0)/(4  0) = 9/4 = 2.25 Answer: B
_________________
Jeffery Miller
Head of GMAT Instruction
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



NonHuman User
Joined: 09 Sep 2013
Posts: 9879

Re: In the xycoordinate system, what is the slope of the line
[#permalink]
Show Tags
17 Oct 2018, 16:57
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: In the xycoordinate system, what is the slope of the line
[#permalink]
17 Oct 2018, 16:57






