Find the point, m, that divides segment ab into a ratio of 2: 3 if a is at (0, 15) and b is at (20, 0).

 The required co-ordinates of point M are (8, 9).

Step-by-step explanation:  Given that the point M divides segment AB into a ratio of 2 : 3, where A is at (0, 15) and B is at (20, 0).

We are to find the co-ordinates of point M.

We know that

the co-ordinates of a point that divides the line segment joining the points (a, b) and (c, d) are given by

For the given division, (a, b) = (0, 15), (c, d) = (20, 0) and m : n = 2 : 3.

Therefore, the co-ordinates of point M are given by

Thus, the required co-ordinates of point M are (8, 9).