BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Ab=2BC. representative of point B

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Legendary Member
Posts: 941
Joined: Sun Dec 27, 2009 12:28 am
Thanked: 20 times
Followed by:1 members

Ab=2BC. representative of point B

by bhumika.k.shah » Sat Feb 27, 2010 2:19 am
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)

Source MGMAT QB
Top
Source: — Problem Solving |
User avatar
GMAT Instructor
Posts: 3650
Joined: Wed Jan 21, 2009 4:27 am
Location: India
Thanked: 267 times
Followed by:80 members
GMAT Score:760

by sanju09 » Sat Feb 27, 2010 2:37 am
bhumika.k.shah 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)

Source MGMAT QB
It's a Section Formula problem (internal division case).

B (x', y') is such that

x' = {m x (#2) + n x (#1)}/ (m + n), and y' = {m y (#2) + n y (#1)}/ (m + n).

In the given situation, x (#1) = 0, x (#2) = 3, y (#1) = -3, y (#2) = 3, and above all, m = 2 and n = 1.

We have to be really careful in assigning values to the formula.

With that, we have x' = (2 × 3 + 1 × 0)/3 = 2, and y' = (2 × 3 + 1 × -3)/3 = 1,

or the coordinates of point B are [spoiler](2, 1)[/spoiler].

[spoiler]C[/spoiler]
The mind is everything. What you think you become. -Lord Buddha



Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com
Top
Master | Next Rank: 500 Posts
Posts: 182
Joined: Sat Apr 11, 2009 4:55 am
Thanked: 11 times

by Giorgio » Wed Mar 24, 2010 4:40 am
Aside from measuring it with eye , is there any other easier way to solve this kind of question?
Top
User avatar
Legendary Member
Posts: 526
Joined: Sat Feb 21, 2009 11:47 pm
Location: India
Thanked: 68 times
GMAT Score:680

by harshavardhanc » Wed Mar 24, 2010 5:40 am
Giorgio wrote:Aside from measuring it with eye , is there any other easier way to solve this kind of question?
Giorgio,

Here is a post in which I've tried to make it easier :

https://www.beatthegmat.com/post232132.html#232132
Regards,
Harsha
Top
Senior | Next Rank: 100 Posts
Posts: 51
Joined: Mon Jul 13, 2009 4:25 pm
Thanked: 1 times

by ymach3 » Wed Mar 24, 2010 10:05 pm
Hi Sanju,

I got B as (1,-1) when i used the Section Formula you mentioned.

I also re-checked the soultion by calculating the distance AB abd BC using B as(1,-1).

AB=root(5)

BC=2root(5)

Could you please check and correct me if i am wrong.
Top
Post new topic Post Reply
• Page 1 of 1