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jabhatta2
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What are the coordinates for the point on Line AB that is 19 Aug 2020, 13:31
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VeritasKarishma -- just wondering how you would solve this problem ?

I can certainly memorize this formula being discussed but preferably would not given i know the GMAT is all about logic.
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rohan994
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What are the coordinates for the point on Line AB that is 21 Aug 2020, 21:25
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The point needs to be 3 times farther from one point than the other,

this implies, the line can be divided in the ratio 1:3 or 4 parts.

This would mean you need to find 2 mid points.

A(-5,6) and B (-2,0).

First midpoint M1 ((-5-2)/2, (6-0)/2 ) = M1 (-3.5,3)

Second mid point needs to be in between B and M1 and hence M2 ((-3.5-2)/2 , (3-0)/2) = M2(-2.75,1.5)
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What are the coordinates for the point on Line AB that is 24 Aug 2020, 01:54
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jabhatta2
VeritasKarishma -- just wondering how you would solve this problem ?

I can certainly memorize this formula being discussed but preferably would not given i know the GMAT is all about logic.
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Yes, you don't need any formulas.

Note that from B to A, x co-ordinate decreases by 3 units and y co-ordinate increases by 6 units.
You need to divide this distance equally into 4 units (3 units away from A and 1 unit away from B).
For each unit, x co-ordinate will decrease by 3/4 and y co-ordinate will increase by 6/4
Since we need 1 unit away from B, x co-ordinate of th required point becomes -2 - 3/4 = -2.75 and y co-ordinate becomes 0 + 6/4 = 1.5

Answer (-2.75, 1.5)
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What are the coordinates for the point on Line AB that is 05 Sep 2020, 12:58
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hoaivinh
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?
Attachment:
mgmat.png

OA:
Show Spoiler
(-2.75, 1.5)
Show more
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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What are the coordinates for the point on Line AB that is 06 Sep 2020, 04:30
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hoaivinh
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?
Attachment:
mgmat.png

OA:
Show Spoiler
(-2.75, 1.5)
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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Hi ScottTargetTestPrep,

First you figured out M (Midpoint) which has to be equidistant from A and B. Then you figured out N (Midpoint of M and B). Then how is N three times as far from A as from B.

Three times as far from A as from B means it has to be 3 times as far from both A as well as B right?

It'll be great if you'd help me understand

Thank you :)

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What are the coordinates for the point on Line AB that is 06 Sep 2020, 04:33
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Narenn
Refer the formula attached in the figure below.

Let P (x,y) be a point on line AB such that AP/PB = 3/1.

Co-ordinate of X = \(\frac{mx2 + nx1}{m + n}\) -----> \(\frac{3(-2) + 1(-5)}{3+1}\) ----------> \(\frac{-6 - 5}{4}\) --------> \(\frac{-11}{4}\)

Co-ordinate of Y = \(\frac{my2 + ny1}{m + n}\) -----> \(\frac{3(0) + 1(6)}{3+1}\) ----------> \(\frac{6}{4}\) -------> \(\frac{3}{2}\)

Hence p(x,y) = \((\frac{-11}{4})\), \((\frac{3}{2})\)

Note the following points about posting.
1) If you want to attach a figure with the post, just copy and paste the figure in MS Paint then save the file as png image. Then simply type the question stem in the post text box and attach the saved png image to the post
2) Post the question in relevant forum. e.g. This question should be posted in GMAT quantitative - Problem solving subforum, and should not be in General GMAT questions.
3) Post the question along with OA.

Hope that helps! :)
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Hi Narenn,

How did you figure out m=3 and n=1?

Secondly, doesn't "Three times as far from A as from B" mean that the point has to be 3 times far from both A as well as B?

Please help me understand if I'm missing out on something.

Thank you. :)

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What are the coordinates for the point on Line AB that is 08 Sep 2020, 19:26
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hoaivinh
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?
Attachment:
mgmat.png

OA:
Show Spoiler
(-2.75, 1.5)
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)

Hi ScottTargetTestPrep,

First you figured out M (Midpoint) which has to be equidistant from A and B. Then you figured out N (Midpoint of M and B). Then how is N three times as far from A as from B.

Three times as far from A as from B means it has to be 3 times as far from both A as well as B right?

It'll be great if you'd help me understand

Thank you :)

Posted from my mobile device
Show more

Three times as far from A as from B means the distance between the point and A is equal to three times the distance between the point and B. So, if the distance between N and B is d, then the distance between N and A should be 3d so that we can say the point N is three times as far from A as from B.
To elaborate further, M is the midpoint of A and B, so the distance between A and M is equal to the distance between M and B. Let's call this distance s. N is the midpoint between M and B, so the distance between M and N is equal to the distance between N and B. Since we already represented the distance between M and B by s, the distance between M and N is s/2 and the distance between N and B is also s/2.
Notice that the distance between A and N is the sum of the distance between A and M and the distance between M and N. The former is s and the latter is s/2, so the distance between A and N is s + s/2 = 3s/2, which is precisely three times the distance between N and B, which is s/2.
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What are the coordinates for the point on Line AB that is 02 Jan 2021, 04:23
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The simplest way to solve this question is by using the midpoint formula. We need to find a point that is 3times as far from A as B. So consider the midpoint of A and B, Let's call this point C((-5+-2)/2; (6+0)/2). Now the midpoint of point C and B will be exactly 3 times as far from A as B. So the midpoint of C & B let's call it D will have the co-ordinates((-3.5-2/2;3-0/2).
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What are the coordinates for the point on Line AB that is 08 Dec 2021, 06:51
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No answer choices in the question! Please edit
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What are the coordinates for the point on Line AB that is 08 Dec 2021, 06:57
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askelan
No answer choices in the question! Please edit
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Done. Thank you.
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What are the coordinates for the point on Line AB that is 23 Feb 2026, 03:59
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