Author 
Message 
TAGS:

Hide Tags

Director
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 521
Location: United Kingdom
Concentration: International Business, Strategy
GPA: 2.9
WE: Information Technology (Consulting)

The coordinates of points A and C are (0, 3) and (3, 3) [#permalink]
Show Tags
18 Feb 2012, 18:31
2
This post received KUDOS
20
This post was BOOKMARKED
Question Stats:
67% (01:37) correct 33% (02:10) wrong based on 722 sessions
HideShow timer Statistics
The coordinates of points A and C are (0, 3) and (3, 3), respectively. If point B lies on line AC between points A and C, and if AB = 2BC, which of the following represents the coordinates of point B? A. (1, 5) B. (1, 1) C. (2, 1) D. (1.5, 0) E. (5, 5) How this can be solved guys?
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Best Regards, E.
MGMAT 1 > 530 MGMAT 2> 640 MGMAT 3 > 610 GMAT ==> 730



Math Expert
Joined: 02 Sep 2009
Posts: 44320

The coordinates of points A and C are (0, 3) and (3, 3) [#permalink]
Show Tags
18 Feb 2012, 18:47
8
This post received KUDOS
Expert's post
2
This post was BOOKMARKED
enigma123 wrote: The coordinates of points A and C are (0, 3) and (3, 3), respectively. If point B lies on line AC between points A and C, and if AB = 2BC, which of the following represents the coordinates of point B?
A. (1, 5) B. (1, 1) C. (2, 1) D. (1.5, 0) E. (5, 5)
How this can be solved guys? Even though it's possible to set an algebraic equation to get the answer, it would be much easier to draw the line segment AC and you will literally see the answer: Attachment:
The coordinates.PNG [ 14.83 KiB  Viewed 37075 times ]
Since AB is twice the length of BC then the only acceptable choices is B (2, 1). Two points (1, 5) and (5, 5) does not lie on AC at all, (1.1) is closer to A than to C and (1.5, 0) divides AC in half. Answer: C.
_________________
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? Extrahard Quant Tests with Brilliant Analytics



Director
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 521
Location: United Kingdom
Concentration: International Business, Strategy
GPA: 2.9
WE: Information Technology (Consulting)

Re: The coordinates of points A and C are (0, 3) and (3, 3) [#permalink]
Show Tags
18 Feb 2012, 19:01
Thanks Bunuel  I didn't get it sorry. How did you arrive at 2 as the coordinate for B? Sorry again. Also, I was trying to solve this by using the distance formula for AC.
_________________
Best Regards, E.
MGMAT 1 > 530 MGMAT 2> 640 MGMAT 3 > 610 GMAT ==> 730



Math Expert
Joined: 02 Sep 2009
Posts: 44320

Re: The coordinates of points A and C are (0, 3) and (3, 3) [#permalink]
Show Tags
18 Feb 2012, 19:05



Intern
Joined: 28 Mar 2011
Posts: 7

Re: The coordinates of points A and C are (0, 3) and (3, 3) [#permalink]
Show Tags
03 Sep 2013, 11:24
Bunuel wrote: enigma123 wrote: The coordinates of points A and C are (0, 3) and (3, 3), respectively. If point B lies on line AC between points A and C, and if AB = 2BC, which of the following represents the coordinates of point B?
A. (1, 5) B. (1, 1) C. (2, 1) D. (1.5, 0) E. (5, 5)
How this can be solved guys? Even though it's possible to set an algebraic equation to get the answer, it would be much easier to draw the line segment AC and you will literally see the answer: Attachment: The coordinates.PNG Since AB is twice the length of BC then the only acceptable choices is C (2, 1). Two points (1, 5) and (5, 5) does not lie on AC at all, (1.1) is closer to A than to C and (1.5 0) divides AC in half. Answer: C. question says AB=2AC and B is the in between point of AC. it can be inferred from that B is the middle point of AC. So, all it need to find out the midpoint of AC. M1= 30/2 = 1.5 M2= 33/2 = 0 So, B (1.5, 0) If I am wrong please correct me.



Math Expert
Joined: 02 Sep 2009
Posts: 44320

Re: The coordinates of points A and C are (0, 3) and (3, 3) [#permalink]
Show Tags
03 Sep 2013, 11:30
zachowdhury wrote: Bunuel wrote: enigma123 wrote: The coordinates of points A and C are (0, 3) and (3, 3), respectively. If point B lies on line AC between points A and C, and if AB = 2BC, which of the following represents the coordinates of point B?
A. (1, 5) B. (1, 1) C. (2, 1) D. (1.5, 0) E. (5, 5)
How this can be solved guys? Even though it's possible to set an algebraic equation to get the answer, it would be much easier to draw the line segment AC and you will literally see the answer: Attachment: The coordinates.PNG Since AB is twice the length of BC then the only acceptable choices is C (2, 1). Two points (1, 5) and (5, 5) does not lie on AC at all, (1.1) is closer to A than to C and (1.5 0) divides AC in half. Answer: C. question says AB=2AC and B is the in between point of AC. it can be inferred from that B is the middle point of AC. So, all it need to find out the midpoint of AC. M1= 30/2 = 1.5 M2= 33/2 = 0 So, B (1.5, 0) If I am wrong please correct me. The questions says that AB = 2BC, not that AB=2 AC.
_________________
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? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 18 Aug 2013
Posts: 18

Re: The coordinates of points A and C are (0, 3) and (3, 3) [#permalink]
Show Tags
03 Sep 2013, 17:51
How would you find the coordinates algebraically?
I've done problems where AB=3BC, so you can easily find the average of two points, then again average the midpoint and C to find the answer, but that is not possible for a problem like this where the ratio of distance is 2:1.
Thanks



Director
Joined: 25 Apr 2012
Posts: 720
Location: India
GPA: 3.21
WE: Business Development (Other)

Re: The coordinates of points A and C are (0, 3) and (3, 3) [#permalink]
Show Tags
03 Sep 2013, 22:14
enigma123 wrote: The coordinates of points A and C are (0, 3) and (3, 3), respectively. If point B lies on line AC between points A and C, and if AB = 2BC, which of the following represents the coordinates of point B?
A. (1, 5) B. (1, 1) C. (2, 1) D. (1.5, 0) E. (5, 5)
How this can be solved guys? For the Graph,please look at Bunuel's post. We can find distance between points A & C using the distance formula : \sqrt{(x2x1)^2 +(y2y1)^2} We get \sqrt{(30)^2+(3(3))^2} > \sqrt{45} Now at point B > AB= 2 BC > AB+BC =\sqrt{45} or 3BC =\sqrt{45} > BC =\sqrt{5} So distance from C to B will be \sqrt{5} Now from answer choice, we can see only option C gives as \sqrt{5} as the distance between Point B and C Bunuel's reply is more crisp and time saving.
_________________
“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”



MBA Section Director
Status: Back to work...
Affiliations: GMAT Club
Joined: 22 Feb 2012
Posts: 5057
Location: India
City: Pune
GPA: 3.4
WE: Business Development (Manufacturing)

Re: The coordinates of points A and C are (0, 3) and (3, 3) [#permalink]
Show Tags
03 Sep 2013, 22:20
15
This post received KUDOS
Expert's post
7
This post was BOOKMARKED
Refer the first case (i.e. Formula for INTERNAL DIVISION) In our case \(\frac{m}{n} = \frac{2}{1}\) AND (x1 y1) = (0,3) (x2 y2) = (3, 3) X Coordinate = \(\frac{2(3)+0}{(1+2)}\) > \(\frac{6}{3}\) > 2 y Coordinate = \(\frac{2(3)+(3)}{(1+2)}\) > \(\frac{3}{3}\) > 1 Hence B (x y) = 2, 1 Refer my this article for brief understanding of this concept.
Attachments
Untitled.png [ 53.89 KiB  Viewed 36195 times ]
_________________
Chances of Getting Admitted After an Interview [Data Crunch]
Must Read Forum Topics Before You Kick Off Your MBA Application
New GMAT Club Decision Tracker  Real Time Decision Updates



Math Expert
Joined: 02 Sep 2009
Posts: 44320

Re: The coordinates of points A and C are (0, 3) and (3, 3), [#permalink]
Show Tags
21 Oct 2013, 10:10
Bunuel wrote: AccipiterQ wrote: The coordinates of points A and C are (0, 3) and (3, 3), respectively. If point B lies on line AC between points A and C, and if AB = 2BC, which of the following represents the coordinates of point B? A (1, \(\sqrt{5}\)) B (1, 1) C (2, 1) D (1.5, 0) E (\(\sqrt{5}\),\(\sqrt{5}\)) could not get this one for the life of me; I calculated what the length of AC was, but after that didn't know how to solve Point B is on line AC, twothirds of the way between Point A and Point C. To find the coordinates of point B, it is helpful to imagine that you are a point traveling along line AC.
When you travel all the way from point A to point C, your xcoordinate changes 3 units (from x = 0 to x = 3). Twothirds of the way there, at point B, your xcoordinate will have changed 2/3 of this amount, i.e. 2 units. The xcoordinate of B is therefore x = 0 + 2 = 2. When you travel all the way from point A to point C, your ycoordinate changes 6 units (from y = 3 to y = 3). Twothirds of the way there, at point B, your ycoordinate will have changed 2/3 of this amount, i.e. 4 units. The ycoordinate of B is therefore y = 3 + 4 = 1.
Thus, the coordinates of point B are (2,1).
The correct answer is C. Merging similar topics. Please refer to the solutions above. Similar question to practice: intherectangularcoordinatesystemabovethelineyx144774.htmlinthexycoordinateplaneispointrequidistantfrom143502.htmlintherectangularcoordinatesystemthelineyxisthe132646.htmlintherectangularcoordinatesystemthelineyxisthe88473.htmlintherectangularcoordinatesystemabovethelineyx129932.htmlthelinerepresentedbytheequationy42xisthe127770.htmlpointsm52andn58lieonthexy127803.htmllinesegmentsabandcdareofequallengthandperpendicula159799.htmlHope it helps.
_________________
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? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 21 Oct 2013
Posts: 193
Location: Germany
GPA: 3.51

Re: The coordinates of points A and C are (0, 3) and (3, 3) [#permalink]
Show Tags
24 Jan 2014, 04:47
1
This post was BOOKMARKED
y = mx + n
n = 3 (from point A) 3 = 3m 3 (from point C) m=2 Equation of line AC: y = 2x  3
Now put in the given answers. None works except from C and D. Both points lie on the line. From the question we know that AB = 2BC. So lets calculate the middle of the line AC. (Xa+Xb)/2 = 0+3 / 2 = 1.5 and (Ya+Yb)/2 = 3+3 / 2 = 0
SO we have M = (1.5;0) which is answer D. Hence answer C is correct.



Director
Joined: 07 Aug 2011
Posts: 577
Concentration: International Business, Technology

The coordinates of points A and C are (0, 3) and (3, 3) [#permalink]
Show Tags
22 Mar 2015, 09:52
enigma123 wrote: The coordinates of points A and C are (0, 3) and (3, 3), respectively. If point B lies on line AC between points A and C, and if AB = 2BC, which of the following represents the coordinates of point B?
A. (1, 5) B. (1, 1) C. (2, 1) D. (1.5, 0) E. (5, 5)
How this can be solved guys? I think this question can be solved without pen and paper . if B were at mid of A and C the coordinates of B were (1.5,0) but we are told that B is closer to C so definitely X coordinate will be more than 1.5 , only 1 point in list of options makes sense . option D . Ignore Option E as it lies outside the line segment AC as we are told that 'point B lies on line AC between points A and C' noticed that there are edits to the option E from (5,5) to ( \(\sqrt{5},\sqrt{5}\)), so possible options are C and E . Slope of line AC=\(\frac{2}{1}\) slope of AB should be same as slope of AC slope of AC = \((\sqrt{5}+3)/(\sqrt{5}  0)\) this cannot be equal to 2.
_________________
Thanks, Lucky
_______________________________________________________ Kindly press the to appreciate my post !!



Senior Manager
Joined: 08 Dec 2015
Posts: 312

The coordinates of points A and C are (0, 3) and (3, 3) [#permalink]
Show Tags
11 Jun 2016, 10:12
1
This post was BOOKMARKED
Want a really long way to solve this? No fancy formulas no estimation on paper. We have from the known coordinates that the big triangle has sides 3, 6, 3BC. So, \(3^2+6^2=3BC^2\) We get that \(bc=\sqrt{5}\) Note that now we have a smaller triangle Then, using the proportions given, so AB=2BC, we can determine that the h of the small triangle is 2. We can also calculate the other side since we know the hypotenuse (\(\sqrt{5}\)) So: \(\sqrt{5}=2^2+x^2\) X=1Then we can use the same concept of proportions AB=2BC to determine that\(\sqrt{5}\) segment corresponds to 1\3rd of the big triangle. So, the distance from origin on Xaxis to the side (base) of the small triangle is 2. And that means that C (2,y). We got our X. Now get the linear equation of the hypotenuse of the big triangle. Using the given points A and B, we get that slope=6/3 or 2 and yintercept is 3So y=2x3Now plugin the X=2 to get that Y=1 Answer C. Logical deduction + Pythagoras Theorem only.
Attachments
triangle 1.jpg [ 21.16 KiB  Viewed 28915 times ]



Manager
Joined: 29 May 2016
Posts: 129

Re: The coordinates of points A and C are (0, 3) and (3, 3) [#permalink]
Show Tags
13 Jul 2016, 23:01
First of all point is closer to C. to get exact coordinates how much distance from y axis will give us X coordinate and distance from x axis will give us Y coordinate difference of Y coordinates of two points 30= 3 now this distance will be divided in such a way that it will give us AB :BC 2:1 ratio. X coordinate will be two. similarly Y ccordinate will be 3(3) = 6 2:1 is 4 is to 2; from 3 it will 4 points that is 1 (2,1)



Manager
Joined: 23 Jul 2015
Posts: 166

Re: The coordinates of points A and C are (0, 3) and (3, 3) [#permalink]
Show Tags
11 Jan 2017, 12:09
Let coordinate of B = \((x_1, y_1)\) Therefore, \(x_1  0 = 2(3  x_1)\) ==>\(3(x_1) = 6\) => \(x_1 = 2\) \(y_1  (3) = 2 (3  y_1)\)==> \(3(y_1) = 6 3\) ==> \(y_1 = 1\) Ans.: C



Director
Joined: 12 Nov 2016
Posts: 790

Re: The coordinates of points A and C are (0, 3) and (3, 3) [#permalink]
Show Tags
14 Jun 2017, 22:18
enigma123 wrote: The coordinates of points A and C are (0, 3) and (3, 3), respectively. If point B lies on line AC between points A and C, and if AB = 2BC, which of the following represents the coordinates of point B?
A. (1, 5) B. (1, 1) C. (2, 1) D. (1.5, 0) E. (5, 5)
How this can be solved guys? For coordinate geometry questions its important to have dry erase grid broad these questions can be more difficult than they need to be and you can end up doing more math then you really need to without a coordinate plane. An dry erase board with a coordinate plane on it can be purchased here https://www.amazon.com/ManhattanGMATS ... %2F+MarkerSecondly, the key word in this question is "coordinate." There is no need to find the distance between point a and c and there is no need to draw out similar triangles with a coordinate plan we could simply draw this on the board now, if AB=2BC then that simply means point B would 2/3 of the height and thus C



Intern
Joined: 09 Oct 2016
Posts: 32

The coordinates of points A and C are (0, 3) and (3, 3) [#permalink]
Show Tags
16 Sep 2017, 07:48
enigma123 wrote: The coordinates of points A and C are (0, 3) and (3, 3), respectively. If point B lies on line AC between points A and C, and if AB = 2BC, which of the following represents the coordinates of point B?
A. (1, 5) B. (1, 1) C. (2, 1) D. (1.5, 0) E. (5, 5)
How this can be solved guys? The length of AC = √((x1x2)^2 )+(y1y2)^2 = √((03)^2 )+(33)^2 = √45 = 3√5 From the question AB = 2BC, this means that AB = 2√5 and BC = √5 By applying the length formula In the multiple choices, the correct answer should give us the right lengths of AB and BC. Choice C does that: AB = √((x1x2)^2 )+(y1y2)^2 = √((02)^2 )+(31)^2 = √20 = 2√5 BC = = √((x1x2)^2 )+(y1y2)^2 = √((32)^2 )+(31)^2 = √5




The coordinates of points A and C are (0, 3) and (3, 3)
[#permalink]
16 Sep 2017, 07:48






