Question

Point A is located at ​(4, 8)​ and point B is located at ​(14, 10)​ . What point partitions the directed line segment ​ AB⎯⎯⎯⎯⎯ ​ into a 1:3 ratio? (612, 812) (9, 9) (1112, 912) (6, 6)

Answer 1

The 1:3 ratio means that the distance from A to the point is 1/4 of the distance from A to B.

The difference of y-coordinates is 10-8 = 2. 1/4 of that is 2·1/4 = 1/2, so the point of interest will have y-coordinate 8 + 1/2 = 8 1/2. This apparently corresponds to the first selection:

... (6 1/2, 8 1/2)