Asegment with endpoints a (2, 6) and c (5, 9) is partitioned by a point b such that ab and bc form a 3: 1 ratio. find b.

(2.33, 6.33)

(3.5, 10.5)

(3.66, 7.66)

(4.25, 8.25)

To answer the given question, determine the differences of the coordinates. Since the ratio of the lengths of the segment (AB/BC) is 3:1, add 3/4 of these differences to the coordinates of point A. The calculations are shown below,
                  abscissa       (3/4)(5 - 2) + 2 = 4.25
                  ordinate        (3/4)(9 - 6) + 6 = 8.25
Thus, the coordinates of the point is (4.25, 8.25).