PGMAT wrote:eagleeye wrote:PGMAT wrote:The coordinates of points A and C are (0, -3) and (3, 3), respectively. If point B lies on line AC between points A and C, and if AB = 2BC, which of the following represents the coordinates of point B?
(1, -)
(1, -1)
(2, 1)
(1.5, 0)
(,)
what is the easiest way to solve this?
[spoiler]OA:C[/spoiler]
This is the fastest and easiest way to solve this:
since B divides A-C in ratio
1:2, B = (
1*(A)+
2*(C))/(
1+2) =( 1*(0,-3) + 2*(3,3))/3
= ((0,-3)+(6,6))/3 = ((0+6),(-3+6))/3 = (6,3)/3 = (2,1)
Let me know if this helps
Hi, thank you for your response. If the question says AB = 2BC, doesn't this imply that point B is dividing the segment in 2:1? A----B--C
You are right PGMAT: It was a typo. I meant to write 2:1.
Here's the general formula to do it.
If the line joining the point A(a1,a2) and B(b1,b2) is divided in the ratio m:n by point C, then coordinates of C are:
(n*A+m*B)/(m+n)
Just to solidify the concept, if C divides the line-segment joining the points (8, 9) and (-7, 4) in the ratio 2 : 3,
coordinates of C are: (3*(8,9) + 2*(-7,4))/(2+3) = 1/5*((24,27)+(-14,8)) = 1/5*(24-14,27+8) = 1/5*(10,35) = (2,7).
If it makes it any easier, you could remember this too, for point C dividing two points into ratio
m:n, C = (n*first point + m*second point)/(m+n).
Let me know if this helps
