What I wanted to ask was that after finding the coordinates of the point my answer was (1/3, -1) now since the ordinate is -ve doesn't that make this an external division? How can it divide the line internally?
This is an MCQ question with options a) (1,1) b (1, 1/3) c) (1/3, 1) d) (-1/3, 1) e) (1/3,-1)
After solving the question I ticked E but the answer sheet I have says the answer is C.
The point divides the line segment $AB$ in the ratio $2:1$. Let the point be $C$. It's clear that the point lies on $AB$. The point is twice as far from $A$ as it is from $B$.
$\Delta x \text{ from A to B } = 2$ $\Delta y \text{ from A to B } = 9$
$2/3 \cdot 2 = 4/3$ and $2/3 \cdot 9 = 6$.
So the coordinates of the point are $(-1 + 4/3, -7 + 6) = (1/3, -1)$ which is the answer.
Probably, the answer sheet is incorrect.