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

Question

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)

Bunuel · Accepted Answer

Look at the diagram below: https://gmatclub.com/forum/download/file.php?id=18607 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. Line segment.png

veergmat · Answer

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

watwazdaquestion · Answer

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

ameyaprabhu · Answer

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?

chetan2u · Answer

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

RussianDude · Answer

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

yosita18 · Answer

smashbiker84 · Answer

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..

Posted from my mobile device

Abhishek009 · Answer

(-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)

Hoozan · Answer

Bunuel  can we draw the image and simply SEE that point (C) will be in Q3 and hence (A) is the answer?

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

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

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