The point dividing the segment joining (2, 3) and (8, 6) in the ratio 1 : 2 (counting from the first point) has coordinates:

1. From (2, 3) to (8, 6) the x-change is 6 and the y-change is 3. 2. The ratio 1 : 2 means the dividing point is 1/(1+2) = 1/3 of the way along. 3. Add 1/3 of the changes: x = 2 + 6/3 = 4; y = 3 + 3/3 = 4. 4. So the point is (4, 4). 5. This matches the textbook example exactly. _Source: SCERT Kerala Std X Mathematics Part-2, Chapter 8-9 (pp 200-219, 2019 ed.)._