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If point A coordinates are (-7, -3) point B coordinates are [#permalink]

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06 Nov 2012, 04:00

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If point A coordinates are (-7, -3) point B coordinates are (8 ,4 ) if C is along the line A-B so that AC = 1/2 CB. What are the coordinates of point C.

A. (-2, - 2/3) B. (2, -2/3) C. (2/3, -2) D. (0, 2) E. (2, 2/3)

If point A coordinates are ( -7 , -3 ) point B coordinates are (8 ,4 ) if C is along the line A-B so that AC = 1/2 CB. What are the coordinates of point C.

A. ( -2 , - 2/3 ) B. ( 2 , -2/3 ) C. ( 2/3 , -2 ) D. ( 0 , 2 ) E. ( 2 , 2/3 )

Look at the diagram below:

Since, AC= 1/2 CB, then AC = 1/3 AB. This implies that point C is closer to A than to B, which on the other hand implies that the x-coordinate of C must be less than (-7+8)/2=0.5. Only D and A fits, but as (0 , 2) is clearly not on line segment AB, then the answer must be A.

Re: If point A coordinates are (-7, -3) point B coordinates are [#permalink]

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06 Nov 2012, 13:08

this question can be answered using intuition. point A (-7, -3) is closer to the origin than point B (8, 4). given that AC = 1/2 AB means distance of AC < distance of CB. therefore C has to be negative x and negative y. only choice A gives this answer

Re: If point A coordinates are (-7, -3) point B coordinates are [#permalink]

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20 Jul 2014, 09:21

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If point A coordinates are (x1=-7, y1=-3) point B coordinates are (x2=8 ,y2=4 ) if C is along the line A-B so that AC = 1/2 CB. What are the coordinates of point C.

A. (-2, - 2/3) B. (2, -2/3) C. (2/3, -2) D. (0, 2) E. (2, 2/3)

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Re: If point A coordinates are (-7, -3) point B coordinates are [#permalink]

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29 Apr 2016, 07:50

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If point A coordinates are (-7, -3) point B coordinates are [#permalink]

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08 May 2016, 18:12

But isn't this assuming the C lies between A and B. What if it divides the line AB externally. How can we know for sure whether C divides the line externally or internally?

If point A coordinates are (x1=-7, y1=-3) point B coordinates are (x2=8 ,y2=4 ) if C is along the line A-B so that AC = 1/2 CB. What are the coordinates of point C.

A. (-2, - 2/3) B. (2, -2/3) C. (2/3, -2) D. (0, 2) E. (2, 2/3)

But isn't this assuming the C lies between A and B. What if it divides the line AB externally. How can we know for sure whether C divides the line externally or internally?

If point A coordinates are (x1=-7, y1=-3) point B coordinates are (x2=8 ,y2=4 ) if C is along the line A-B so that AC = 1/2 CB. What are the coordinates of point C.

A. (-2, - 2/3) B. (2, -2/3) C. (2/3, -2) D. (0, 2) E. (2, 2/3)

hi, the Q gives you this info- " if C is along the line A-B so that AC = 1/2 CB" _________________

If point A coordinates are (-7, -3) point B coordinates are [#permalink]

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11 Jul 2016, 20:49

Bunuel wrote:

Jp27 wrote:

If point A coordinates are ( -7 , -3 ) point B coordinates are (8 ,4 ) if C is along the line A-B so that AC = 1/2 CB. What are the coordinates of point C.

A. ( -2 , - 2/3 ) B. ( 2 , -2/3 ) C. ( 2/3 , -2 ) D. ( 0 , 2 ) E. ( 2 , 2/3 )

Look at the diagram below:

Attachment:

Line segment.png

Since, AC= 1/2 CB, then AC = 1/3 AB. This implies that point C is closer to A than to B, which on the other hand implies that the x-coordinate of C must be less than (-7+8)/2=0.5. Only D and A fits, but as (0 , 2) is clearly not on line segment AB, then the answer must be A.

Answer: A.

Hope it's clear.

Quote:

Bunuel sir, How did you derive get the following calculation: X-coordinate of C must be less than (-7+8)/2=0.5

As the distance between two points say A(x1, y1) and B (x2, y2) = \sqrt{(x2-x1)^2 + (y2-y1)^2}

Please share your thoughts. Thanks again!

Regards, Yosita

PS: Please forgive me if the format of my post in incorrect.

Re: If point A coordinates are (-7, -3) point B coordinates are [#permalink]

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13 Jul 2016, 21:55

Also, I would like to add that...the answer choices inferentially tell us that point C divides AB internally coz otherwise the coordinates for C would either be farther away from A or B..

Re: If point A coordinates are (-7, -3) point B coordinates are [#permalink]

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04 Sep 2017, 16:45

Hello from the GMAT Club BumpBot!

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