It is currently 14 Dec 2017, 05:25

Decision(s) Day!:

CHAT Rooms | Wharton R1 | Stanford R1 | Tuck R1 | Ross R1 | Haas R1


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 coordinates of points A and C are (0, -3) and (3, 3), respectively

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

Hide Tags

Intern
Intern
User avatar
Joined: 15 Nov 2010
Posts: 4

Kudos [?]: 13 [0], given: 0

The coordinates of points A and C are (0, -3) and (3, 3), respectively [#permalink]

Show Tags

New post 31 Jul 2011, 08:20
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

52% (01:41) correct 48% (01:53) wrong based on 52 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)

[Reveal] Spoiler: My take
No OA provided. I got the answer as B. The approach i adopted:

Found the distance between AC. Then split the distance in 1:2 ratio. Then using the distance formula solved for AB and BC, to find the coordinates of B.

Is this the best approach, or is there a better approach
[Reveal] Spoiler: OA

Kudos [?]: 13 [0], given: 0

BSchool Thread Master
avatar
Joined: 19 Feb 2010
Posts: 390

Kudos [?]: 205 [0], given: 76

Re: The coordinates of points A and C are (0, -3) and (3, 3), respectively [#permalink]

Show Tags

New post 31 Jul 2011, 08:36
I used similar approach, but you don't really need to find the distance between points A and C. For coordinate geometry problems I usually find it useful to quickly draw the graphic so you realize fast how to solve it.
In this case, the distance on x is 3, so 1/3 between 0 and 3 will be 1. And the "height" between A and C is 6, so 1/3 is 2 from the bottom. -3+2=-1. The point is (1,-1).

Kudos [?]: 205 [0], given: 76

Manager
Manager
avatar
Joined: 07 Jun 2011
Posts: 67

Kudos [?]: 11 [0], given: 31

Re: The coordinates of points A and C are (0, -3) and (3, 3), respectively [#permalink]

Show Tags

New post 31 Jul 2011, 19:45
i got answer D

B is at the mid point on line AC, that is why 2BC = AC

find distance AD. Imagine a right triangle with hypotenuse = root base^2 + Altitude ^2

here base = distance on X axis = distance b/w X = 0 and X = 3. Base = 3
Altitude = distance on Y asis = distance b/w Y = - 3 and Y = 3. Altitude = 6

applying the formula we get AC = 3 root 5

now half of AC should be 3/2 root 5

the only answer that satisfy is D. ( calculate BC using the same approach above)

Kudos [?]: 11 [0], given: 31

1 KUDOS received
BSchool Thread Master
avatar
Joined: 19 Feb 2010
Posts: 390

Kudos [?]: 205 [1], given: 76

Re: The coordinates of points A and C are (0, -3) and (3, 3), respectively [#permalink]

Show Tags

New post 01 Aug 2011, 06:56
1
This post received
KUDOS
manishgeorge,

there is no way D could be the answer. the stem of the question does not say that B is at the mid point on the line AC, and 2BC can never be = AC.

If AB = 2BC, it means that the AB segment is two times the length of BC. Or if you divide the segment AC in 3, two portions will correspond to AB, and only one to BC.

See the picture below. You don't need to know the distances on the hypotenuse, but rather the distances in the X axis. The blue portion means the distance AB, in the X axis from 0 to 2. The green portion is BC, in the X axis from 2 to 3. That way, two times BC will be the same as AB.

Now, graphically you can see that the point B is located in (2,1), then the correct answer is C (and I correct myself from my previous post).
Attachments

AB 2BC.jpg
AB 2BC.jpg [ 10.14 KiB | Viewed 2799 times ]

Kudos [?]: 205 [1], given: 76

Intern
Intern
avatar
Joined: 18 Jul 2011
Posts: 43

Kudos [?]: 18 [0], given: 2

Re: The coordinates of points A and C are (0, -3) and (3, 3), respectively [#permalink]

Show Tags

New post 01 Aug 2011, 08:59
BTW, you don't need the distance formula to solve this. The base and height of the Pythagorean triangle formed by (0, -3), (3, -3) and (3, 3) are both divisible by 3. Two thirds of the base = 2 and two thirds of the height = 4. (0, -3) + (2, 4) = (2, 1). C.

Kudos [?]: 18 [0], given: 2

Intern
Intern
avatar
Joined: 14 Mar 2010
Posts: 16

Kudos [?]: 9 [0], given: 1

Re: The coordinates of points A and C are (0, -3) and (3, 3), respectively [#permalink]

Show Tags

New post 19 Aug 2011, 20:44
the x and y coordinates of a point which dived the line with endpoints (x1,y1 ) and (x2, y2 ) in the ratio r:s is
((rX2+sX2)/(r+s) , (rY2+sY1)/(r+s) )

Kudos [?]: 9 [0], given: 1

VP
VP
User avatar
S
Status: Top MBA Admissions Consultant
Joined: 24 Jul 2011
Posts: 1354

Kudos [?]: 663 [0], given: 20

GMAT 1: 780 Q51 V48
GRE 1: 1540 Q800 V740
Re: The coordinates of points A and C are (0, -3) and (3, 3), respectively [#permalink]

Show Tags

New post 02 Sep 2011, 01:48
Point B divides AC in the ratio of 2:1 internally. We can use the section formula to get the coordinates of point B. The section formula says that if a point X divides the line joining A(x1,y1) and B(x2,y2) in the ratio m:n, then the coordinates of X are {m(x2)+n(x1)}/m+n, {m(y2)+n(y1)}/m+n

Therefore the coordinates of point B are {2(3) + 1(0)}/3, {2(3)+1(-3)}/3 = (2,1)
These are the coordinates of option (C), which is the correct answer.
_________________

GyanOne | Top MBA Rankings and MBA Admissions Blog

Top MBA Admissions Consulting | Top MiM Admissions Consulting

Premium MBA Essay Review|Best MBA Interview Preparation|Exclusive GMAT coaching

Get a FREE Detailed MBA Profile Evaluation | Call us now +91 98998 31738

Kudos [?]: 663 [0], given: 20

Manager
Manager
avatar
Joined: 09 Jun 2011
Posts: 105

Kudos [?]: 66 [0], given: 0

Re: The coordinates of points A and C are (0, -3) and (3, 3), respectively [#permalink]

Show Tags

New post 02 Sep 2011, 06:38
Hi GMAT Club! coordinate Geometry is Tough for me. Will you please suggest me the best way to crack Coordinate Geometry?

Kudos [?]: 66 [0], given: 0

Math Forum Moderator
avatar
Joined: 20 Dec 2010
Posts: 1949

Kudos [?]: 2138 [0], given: 376

Re: The coordinates of points A and C are (0, -3) and (3, 3), respectively [#permalink]

Show Tags

New post 02 Sep 2011, 07:35
bholakc wrote:
Hi GMAT Club! coordinate Geometry is Tough for me. Will you please suggest me the best way to crack Coordinate Geometry?


Please go through this at least:
math-coordinate-geometry-87652.html
_________________

~fluke

GMAT Club Premium Membership - big benefits and savings

Kudos [?]: 2138 [0], given: 376

Intern
Intern
avatar
B
Joined: 14 Nov 2012
Posts: 19

Kudos [?]: 4 [0], given: 228

The coordinates of points A and C are (0, -3) and (3, 3), respectively [#permalink]

Show Tags

New post 31 Oct 2017, 17:36
ghostdude 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)


[/spoiler]


Plz not be bothered by my poor drawing :D
We can find the answer without actually calculating C coordination.
In the below picture, let's G be the point at (0,3), F (3,0) and E the interception between AC and Ox.
In triangle AGC, we have OG = OA = 3 and G is 90 degree
=> OE is the midsegment, and E should divide AC into 2 equal parts.
The midsegment is always half the length of its third side, so we have OE = (1/2)GC
As GC = OF, so OE = (1/2) OF = 3/2 = 1.5
OE = 1.5 mean E has coordination of (1.5, 0)
Now here's is the interesting part.
Compare:
AB = 2 BC
AE = EC
=> the x-coordinate of B should be between 1.5 and 3.
=> We can rule out option A, B and D.
Now we check C & E.
Option E: x-coordinate = y-coordinate = \sqrt{5} => B will lie on line segment y=x that go through origin.
Look, point C also has x-coordinate = y-coordinate, so it means O, C, B, A will be on the same straight line, which is obviously wrong.
So we are left with C as the final answer.
Attachments

Untitled.gif
Untitled.gif [ 4.32 KiB | Viewed 265 times ]

Kudos [?]: 4 [0], given: 228

Manager
Manager
avatar
S
Joined: 15 Feb 2017
Posts: 74

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

Re: The coordinates of points A and C are (0, -3) and (3, 3), respectively [#permalink]

Show Tags

New post 31 Oct 2017, 20:46
IMO Option C
Point B divides AC in the ratio of 2:1 internally.
Therefore the coordinates of point B are {2(3) + 1(0)}/3, {2(3)+1(-3)}/3 = (2,1)
These are the coordinates of option (C), which is the correct answer.

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

Director
Director
avatar
P
Joined: 14 Nov 2014
Posts: 622

Kudos [?]: 112 [0], given: 46

Re: The coordinates of points A and C are (0, -3) and (3, 3), respectively [#permalink]

Show Tags

New post 31 Oct 2017, 21:04
There is a section formula for this ..
(Mx2 + Nx1)/M+N where X1 and X2 is coordinate , ratio = M:N
(My2 + NY2)/M+N

Kudos [?]: 112 [0], given: 46

Re: The coordinates of points A and C are (0, -3) and (3, 3), respectively   [#permalink] 31 Oct 2017, 21:04
Display posts from previous: Sort by

The coordinates of points A and C are (0, -3) and (3, 3), respectively

  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®.