Coordinate Plane Problem #2

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C: Junior | Next Rank: 30 Posts; Posts: 23; Joined: Mon Feb 08, 2010 8:19 am; Location: Norway; Thanked: 1 times

Coordinate Plane Problem #2

by C » Mon Mar 22, 2010 12:05 am

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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?

A=(-5,6) B=(-2,0)

Source is MGMAT Geometry. No answer choices were given, OA is [spoiler](-2,75, 1,5)[/spoiler]

Explanation is appreciated.

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Source: Beat The GMAT — Problem Solving | Mon Mar 22, 2010 12:05 am

kstv: Legendary Member; Posts: 610; Joined: Fri Jan 15, 2010 12:33 am; Thanked: 47 times; Followed by:2 members

by kstv » Mon Mar 22, 2010 12:40 am

This test a specific formula

If point C divides the line A B where coordinate of A is (x,y) and B is (x1,y1) in the ratio 3:1 or m:n
then the x coordinate is point C ( mx1+nx/m+n) so in this example x will be (3x-2+1x-5/3+1) = -11/4 = -2.75
y coordinate of C is (my1+nx/m+n)
Usually the answer choice wil be given to make a educated guess otherwise we have to remember one more formula which is not fair.

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neoreaves: Master | Next Rank: 500 Posts; Posts: 208; Joined: Sun Sep 28, 2008 12:30 pm; Thanked: 22 times

by neoreaves » Mon Mar 22, 2010 1:53 am

Let my try to do this using similar triangles. I hope this gives the right answer

So based on my attached image. It appears that the triangles will be similar. So to calculate the (x,y) we need to just use the 3:4 ratio.

x coodinate --> -5 + ( 3/4) * 3 = -5 + 2.25= - 2.75
y coodinate --> 6 - (3/4)*6 = 1.5 (*note: we subtract because look at the diagram y is decreasing)

Thus IMO (x,y) = (-2.75,1.5). I hope this is the right answer. C Can you please confirm ?

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harshavardhanc: Legendary Member; Posts: 526; Joined: Sat Feb 21, 2009 11:47 pm; Location: India; Thanked: 68 times; GMAT Score:680

by harshavardhanc » Mon Mar 22, 2010 2:06 am

C 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?

A=(-5,6) B=(-2,0)

Source is MGMAT Geometry. No answer choices were given, OA is [spoiler](-2,75, 1,5)[/spoiler]

Explanation is appreciated.

As the above posters have said, section formula can be used to find out the coordinates.

Here is a link in which I have tried to make it easier to apply this formula :

https://www.beatthegmat.com/post232132.html#232132

Regards,
Harsha

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

Re: Coordinate Plane Problem #2

by Scott@TargetTestPrep » Mon Aug 24, 2020 9:46 am

C wrote: ↑
Mon Mar 22, 2010 12:05 am
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?

A=(-5,6) B=(-2,0)

Source is MGMAT Geometry. No answer choices were given, OA is [spoiler](-2,75, 1,5)[/spoiler]

Explanation is appreciated.

Solution:

First we can find M, the midpoint of A and B:

M = ((-5 + (-2))/2, (6 + 0)/2) = (-7/2, 3)

Next, we find N, the midpoint of M and B:

N = (-7/2 + (-2))/2, (3 + 0)/2) = (-11/4, 3/2)

Notice that now N is three times as far from A as from B.

Answer: (-11/4, 3/2)

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