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.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards