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If point A coordinates are (7, 3) point B coordinates are [#permalink]
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06 Nov 2012, 03:00
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If point A coordinates are (7, 3) point B coordinates are (8 ,4 ) if C is along the line AB 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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If point A coordinates are (7, 3) point B coordinates are [#permalink]
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06 Nov 2012, 03:27
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Jp27 wrote: If point A coordinates are ( 7 , 3 ) point B coordinates are (8 ,4 ) if C is along the line AB 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 xcoordinate 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. Attachment:
Line segment.png [ 10.65 KiB  Viewed 5150 times ]
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Re: If point A coordinates are (7, 3) point B coordinates are [#permalink]
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06 Nov 2012, 12:08
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



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If point A coordinates are (7, 3) point B coordinates are [#permalink]
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25 Mar 2015, 10:45
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Simply need to put the data in the formula below x= (mx1+nx2)/(m+n) =(7*2+8*1)/(2+1) = 2 Y= (my1+ny2)/(m+n) =(3*2+4*1)/(2+1) =2/3 AC=m , CB =n Jp27 wrote: If point A coordinates are (x1=7, y1=3) point B coordinates are (x2=8 ,y2=4 ) if C is along the line AB 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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08 May 2016, 17:12
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? veergmat wrote: Simply need to put the data in the formula below x= (mx1+nx2)/(m+n) =(7*2+8*1)/(2+1) = 2 Y= (my1+ny2)/(m+n) =(3*2+4*1)/(2+1) =2/3 AC=m , CB =n Jp27 wrote: If point A coordinates are (x1=7, y1=3) point B coordinates are (x2=8 ,y2=4 ) if C is along the line AB 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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08 May 2016, 19:10
ameyaprabhu wrote: 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? veergmat wrote: Simply need to put the data in the formula below x= (mx1+nx2)/(m+n) =(7*2+8*1)/(2+1) = 2 Y= (my1+ny2)/(m+n) =(3*2+4*1)/(2+1) =2/3 AC=m , CB =n Jp27 wrote: If point A coordinates are (x1=7, y1=3) point B coordinates are (x2=8 ,y2=4 ) if C is along the line AB 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 AB so that AC = 1/2 CB"
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If point A coordinates are (7, 3) point B coordinates are [#permalink]
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30 Jun 2016, 05:13
coordinates of A (7; 3) coordninates of B (8; 4) since, line AB consists of three equal segments: 7 + 3m = 8 hence, m = 5 3 + 3n = 4 hence, n = 7/3 xcoordinate of C = xcoordinate of A + m = 7 + 5 = 2 ycoordinate of C = ycoordinate of A + n =  3 + 7/3 =  2/3 Answer A
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If point A coordinates are (7, 3) point B coordinates are [#permalink]
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11 Jul 2016, 19:49
Bunuel wrote: Jp27 wrote: If point A coordinates are ( 7 , 3 ) point B coordinates are (8 ,4 ) if C is along the line AB 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 xcoordinate 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: Xcoordinate 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{(x2x1)^2 + (y2y1)^2}
Please share your thoughts. Thanks again!
Regards, Yosita
PS: Please forgive me if the format of my post in incorrect.



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Re: If point A coordinates are (7, 3) point B coordinates are [#permalink]
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13 Jul 2016, 20:55
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..
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Re: If point A coordinates are (7, 3) point B coordinates are [#permalink]
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