Problem Solving

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?

A . (1, -sqrt 5 )
B. (1, -1)
C. (2, 1)
D. (1.5, 0)
E. (sqrt 5,sqrt 5)

Source MGMAT QB

bhumika.k.shah 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?

A . (1, -sqrt 5 )
B. (1, -1)
C. (2, 1)
D. (1.5, 0)
E. (sqrt 5,sqrt 5)

Source MGMAT QB

It's a Section Formula problem (internal division case).

B (x', y') is such that

x' = {m x (#2) + n x (#1)}/ (m + n), and y' = {m y (#2) + n y (#1)}/ (m + n).

In the given situation, x (#1) = 0, x (#2) = 3, y (#1) = -3, y (#2) = 3, and above all, m = 2 and n = 1.

We have to be really careful in assigning values to the formula.

With that, we have x' = (2 × 3 + 1 × 0)/3 = 2, and y' = (2 × 3 + 1 × -3)/3 = 1,

or the coordinates of point B are [spoiler](2, 1)[/spoiler].

[spoiler]C[/spoiler]

Aside from measuring it with eye , is there any other easier way to solve this kind of question?

Giorgio wrote:Aside from measuring it with eye , is there any other easier way to solve this kind of question?

Giorgio,

Here is a post in which I've tried to make it easier :

https://www.beatthegmat.com/post232132.html#232132

Hi Sanju,

I got B as (1,-1) when i used the Section Formula you mentioned.

I also re-checked the soultion by calculating the distance AB abd BC using B as(1,-1).

AB=root(5)

BC=2root(5)

Could you please check and correct me if i am wrong.