Coordinate Plane Problem #2

This test a specific formula

If point C divides the line A B where coordinate of A is (x,y) and B is (x1,y1) in the ratio 3:1 or m:n
then the x coordinate is point C ( mx1+nx/m+n) so in this example x will be (3x-2+1x-5/3+1) = -11/4 = -2.75
y coordinate of C is (my1+nx/m+n)
Usually the answer choice wil be given to make a educated guess otherwise we have to remember one more formula which is not fair.

Let my try to do this using similar triangles. I hope this gives the right answer



So based on my attached image. It appears that the triangles will be similar. So to calculate the (x,y) we need to just use the 3:4 ratio.


x coodinate --> -5 + ( 3/4) * 3 = -5 + 2.25= - 2.75
y coodinate --> 6 - (3/4)*6 = 1.5 (*note: we subtract because look at the diagram y is decreasing)

Thus IMO (x,y) = (-2.75,1.5). I hope this is the right answer. C Can you please confirm ?

C wrote:What are the coordinates for the point on Line AB (see figure) that is three times as far from A as from B, and that is in between points A and B?

A=(-5,6) B=(-2,0)


Source is MGMAT Geometry. No answer choices were given, OA is [spoiler](-2,75, 1,5)[/spoiler]

Explanation is appreciated.

As the above posters have said, section formula can be used to find out the coordinates.

Here is a link in which I have tried to make it easier to apply this formula :

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