A point T on a segment with endpoints D (1.4) and F (7.1) partitions the segment in a 3:1 ratio. Find T. You must show all work to receive credit.

Given:

A point T on a segment with endpoints D (1,4) and F (7,1) partitions the segment in a 3:1 ratio.

To find:

The coordinates of point T.

Solution:

Section formula: If a point divided a line segment whose end points are and in m:n, then the coordinates of that point are

A point T on a segment with endpoints D (1,4) and F (7,1) partitions the segment in a 3:1 ratio.

Using section formula, we get

Therefore, the coordinates of point T are (5.5, 1.75).