Question

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.

a) (4, 3)
b) (3, 4)
c) (5, 2)
d) (2, 5)

Answer 1

To find the point T that partitions the segment DF in a 3:1 ratio, use the formula ((3*D) + (1*F)) / (3 + 1) and plug in the coordinates for D and F.

Step-by-step explanation:

To find the point T that partitions the segment DF in a 3:1 ratio, we can use the formula:

T = ((3*D) + (1*F)) / (3 + 1)

Plugging in the coordinates for D and F, we have:

T = ((3*1, 4) + (1*7, 1)) / (3 + 1)

T = (3 + 7, 12 + 1) / 4

T = (10, 13) / 4

T = (10/4, 13/4)

So, the point T is (2.5, 3.25).