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

Redeem

Need help with this too!

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Problem Solving |
User avatar
Master | Next Rank: 500 Posts
Posts: 283
Joined: Sun Jun 23, 2013 11:56 pm
Location: Bangalore, India
Thanked: 97 times
Followed by:26 members
GMAT Score:750

by ganeshrkamath » Sun Aug 25, 2013 8:21 am
yumi2012 wrote:What are the coordinates for the point on Line AB (see figure) that is three times as far from A as from B, and that is in between points A and B?
Image
Equation of the line is y/(x+2) = 6/(-5+2)
=> y/(x+2) = -2____________________(1)

Distance between A and B = sqrt((-5-(-2))^2 + (6-0)^2) = sqrt(9+36) = sqrt(45)
Distance between new point C and B = sqrt(45)/4
sqrt(45)/4 = sqrt((x+2)^2 + y^2)
45/16 = (x+2)^2 + y^2

From (1), (x+2) = -y/2
45/16 = (-y/2)^2 + y^2
45/16 = y^2/4 + y^2
45/16 = 5y^2/4
y^2 = 9/4
y = 3/2
x = -(3/2)/2 - 2
x = -3/4 - 2
x = -11/4

So the coordinates of the point are [spoiler](-11/4, 3/2)[/spoiler]

Cheers

PS: Please give the options the next time you post a question.
Every job is a self-portrait of the person who did it. Autograph your work with excellence.

Kelley School of Business (Class of 2016)
GMAT Score: 750 V40 Q51 AWA 5 IR 8
https://www.beatthegmat.com/first-attemp ... tml#688494
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Sun Aug 25, 2013 8:49 am
yumi2012 wrote:What are the coordinates for the point on Line AB (see figure) that is three times as far from A as from B, and that is in between points A and B?
Image
Here's a different approach.
Consider the right triangle with AB as the hypotenuse.
Image

Now divide the two legs into 4 parts.
Image

If we draw a right triangle like so, we'll see that the red triangle is 1/4 the size of the original blue triangle.
Image

IMPORTANT: This means that the distance from A to C is THREE TIMES the distance from C to B. So, point C satisfies the given information.

Now all we need to do is determine the size of the red triangle.
Image

Since the red triangle is 1/4 the size of the blue triangle, its sides have lengths 3/4 and 1 1/2.
So, to the find the coordinates of C, just factor these lengths into the coordinates of point B.

So, the x-coordinate of point C = (-2) - (3/4) = -2 3/4 (aka -2.75)
The y-coordinate of point C = (0) + (1 1/2) = 1 1/2 (aka 1.5)

So the coordinates are [spoiler](-2.75, 1.5)[/spoiler]

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Post new topic Post Reply
• Page 1 of 1