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by prashanthichennupati » Sat Aug 17, 2013 7:15 pm
What are the coordinates for the point on line AB that is 3 times as far from A as from B, and that is between points A and B, knowing that A = (-5,6) and B (-2,0)?

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by melguy » Sat Aug 17, 2013 9:48 pm
Hi prashanthichennupati

Please provide the answer choices.
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by GMATGuruNY » Sun Aug 18, 2013 3:54 am
prashanthichennupati wrote:What are the coordinates for the point on line AB that is 3 times as far from A as from B, and that is between points A and B, knowing that A = (-5,6) and B (-2,0)?
Let C = the unknown point.
The GMAT would provide answer choices.
Only one of these answer choices is likely to be viable.
Thus, there would be no need to calculate the exact coordinates of point C.

DRAW the figure, plotting C so that it is 3 times as far from A as from B.
Image

The figure above indicates that the x-coordinate of point C must be between -2 and -3 and that the y-coordinate of point C must be between 1 and 2.
Select the appropriate answer choice.

An official problem that tests this concept and that can be solved quickly without calculating:
https://www.beatthegmat.com/coordinate-g ... 58176.html

An even trickier official problem that can be solved quickly without calculating:
https://www.beatthegmat.com/og-12-t77036.html

Similar non-official problems:
https://www.beatthegmat.com/grockit-toug ... 74452.html
https://www.beatthegmat.com/cant-form-th ... 67741.html
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by [email protected] » Sun Aug 18, 2013 12:27 pm
Hi prashanthichennupati,

Both melguy and Mitch are correct in that having the answer choices would make this question considerably easier to answer.

To add a point about graphing though, you'll notice (using Mitch's drawing) that any diagonal line on a graph is part of a right triangle (that you can draw). You'll notice that this right triangle has a base of 3 and a height of 6, so you could use the Pythagorean Theorem to figure out the length of that diagonal (if you needed to figure it out) and then figure out how far up or down that line you'd need to go to find your mystery co-ordinate.

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by tarik » Mon Aug 19, 2013 4:08 pm
thank you Mitch you are a great help
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by Sul » Wed Aug 21, 2013 3:11 am
Hi

guys can you please confirm if my methodology is correct for this question?
Since the point is divided into ratio of 3:1

x coordinate = ((-2)*3+1*(-5))/4= -2.75 , y coordinate = ((0*3)=1*6)/4 = 1.5


[email protected] wrote:Hi prashanthichennupati,

Both melguy and Mitch are correct in that having the answer choices would make this question considerably easier to answer.

To add a point about graphing though, you'll notice (using Mitch's drawing) that any diagonal line on a graph is part of a right triangle (that you can draw). You'll notice that this right triangle has a base of 3 and a height of 6, so you could use the Pythagorean Theorem to figure out the length of that diagonal (if you needed to figure it out) and then figure out how far up or down that line you'd need to go to find your mystery co-ordinate.

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Rich
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by [email protected] » Wed Aug 21, 2013 12:00 pm
Hi Sul,

Yes, your math is correct. Remember though that the GMAT often provides shortcuts (in the answers themselves) that can help you to avoid doing unnecessary math.

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