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?
(9, 9)
(6 1/2, 8 1/2) (6, 6) (11 1/2, 9 1/2)

Answer 1

The point can be found as the weighted average of the given points, with the weights being the reverse of the line segment ratio values. The dividing point D will be

... D = (3*(4, 8) + 1*(14, 10))/(3 + 1) = (12+14, 24+10)/4

... D = (6 1/2, 8 1/2) . . . . . matches your second selection