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If point A coordinates are (-7, -3) point B coordinates are

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Jp27
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If point A coordinates are (-7, -3) point B coordinates are [#permalink] New post   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)
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A
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Bunuel
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If point A coordinates are (-7, -3) point B coordinates are [#permalink] New post   06 Nov 2012, 04:27
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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 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.

Answer: A.

Hope it's clear.

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Attachment:
Line segment.png
Line segment.png [ 10.65 KiB | Viewed 14767 times ]
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veergmat
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If point A coordinates are (-7, -3) point B coordinates are [#permalink] New post   25 Mar 2015, 11:45
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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

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

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

:idea:
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 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] New post   08 May 2016, 20:10
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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

:idea:
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 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"
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If point A coordinates are (-7, -3) point B coordinates are [#permalink] New post   30 Jun 2016, 06:13
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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

x-coordinate of C = x-coordinate of A + m = -7 + 5 = -2

y-coordinate of C = y-coordinate 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] New post   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.

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

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Re: If point A coordinates are (-7, -3) point B coordinates are [#permalink] New post   25 Nov 2020, 08:10
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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 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)

(-7 , -3)___________________________________________(8 , 4)
A_________________C_______________________________B
________1_____________________2___________________

Coordinate of Point C is \(\frac{mx_2 + nx_1}{m + n}\) , \(\frac{my_2 + ny_1}{m + n}\) = \(\frac{1*8 + 2(-7)}{1+2} , \frac{1*4 + 2(-3)}{1+2} = (-2, - 2/3) \), Answer must be (A)
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Re: If point A coordinates are (-7, -3) point B coordinates are [#permalink] New post   07 Feb 2022, 00:52
Bunuel can we draw the image and simply SEE that point (C) will be in Q3 and hence (A) is the answer?
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Re: If point A coordinates are (-7, -3) point B coordinates are [#permalink] New post   07 Feb 2022, 01:38
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Hoozan wrote:
Bunuel can we draw the image and simply SEE that point (C) will be in Q3 and hence (A) is the answer?


Yes, if you can identify that that C must be in the third quadrant, then only A remains and thus it must be correct.
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Re: If point A coordinates are (-7, -3) point B coordinates are [#permalink] New post   25 Dec 2023, 02:37
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Re: If point A coordinates are (-7, -3) point B coordinates are [#permalink]
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