The endpoints of segment ac are a( – 7, – 3) and c( 8, 4). point b is somewhere in between ac. determine the coordinates of point b if the ratio of the distances between these points is ab : bc = 5 : 2.

The horizontal distance between AC is 15 units
The vertical distance between AC is 7 units

The point B is located such that AB: BC = 5:2, in other words, AB = 5/7 of the line and BC is 2/7 of the line

5/7 of the horizontal distance is (5/7) × 15 = 75/7
2/7 of the vertical distance is (2/7) × 15 = 30/7

The coordinate of B is (75/7, 30/7)