Find the coordinates of P so that P partitions the segment AB in the ratio 1:3 if A(5,8) and B(−1,4)

Answer 1

There are 2 possible answers depending on whether the long segment is closer to A or B.

The ratio of 1:3 means there must be 4 equal parts of the line, 1 part in one segment and 3 parts in the other

One answer is:

(1/4)5 + (3/4)(-1) = 1/2

(1/4)8 + (3/4)4 = 5/4

i.e.

[(1/2),(5/4)]