Question

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).

Answer 1

What is segment ab? is there a picture that is supposed to go with it?

Answer 2

Answer:  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

$\left(\dfrac{mc+na}{m+n},\dfrac{md+nb}{m+n}\right).$

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

$\left(\dfrac{2\times20+3\times0}{2+3},\dfrac{2\times0+3\times15}{2+3}\right)\\\\\\=\left(\dfrac{40}{5},\dfrac{45}{5}\right)\\\\\\=\left(8,9).$

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