Determine The Points Of Trisection Of The Line Segment Joining The Points P1 (3,-2) And P2 (9,6)?

The x dimensions differ by 9-3=6, so each point will have an x coordinate different from the others by 6/3 = 2.
The y dimensions differ by 6-(-2)= 8, so each point will have a y coordinate different from the others by 8/3 = 2 2/3.
The two points you seek are
  (3, -2) + (2, 2 2/3) = (5, 2/3)   (9, 6) - (2, 2 2/3) = (7, 3 1/3)