Question

point M divides AB so that AM:MB 1:2. If A has coordinates (-1,-3) and B has coordinates (8,9), what are the coordinates of M?

Answer 1

The coordinates of point M are (2,1)

Explanation:

Let's call the coordinates of point M by (x, y)

We have that the rate AM:MB is 1/2, so we can calculate x and y as follows:

x-coordinate of A is equal to -1, and x-coordinate of B is equal to 8, then:

AM:MB = [x - (-1)] / [8 - x] = 1/2

(x+1)/(8-x) = 1/2

2x+2 = 8-x

3x = 6

x = 2

y-coordinate of A is equal to -3, and y-coordinate of B is equal to 9, then:

AM:MB = [y - (-3)] / [9 - y] = 1/2

(y+3)/(9-y) = 1/2

2y+6 = 9-x

3y = 3

y = 1

So the coordinates of point M are x = 2 and y = 1 or (2,1)