What is the location of point f, which partitions the directed line segment from d to e into a 4: 5 ratio? –3 0 1 4

You haven't provided the coordinates of points D and E, therefore, I can only help with the concept.

I'll tell you how to solve such problem and you substitute in the equation with the numbers you have.

The formulas given to calculated the x and y coordinates are as follows:

Let's define the variables used:

(x₁ , y₁) are the coordinates of the first point while (x₂ , y₂) are the coordinates of the second point.

We are given that the segment is directed from D to E, therefore:

First point is D ..........> (x₁ , y₁) are coordinates of point D

Second point is E ....> (x₂ , y₂) are coordinates of point E

m and n defined the portion of the partitioned segment (DF : FE). It is given that this ratio is 4:5. Therefore:

m = 4 and n = 5

Substitute the values in the above equation and you'll get your answer.

Hope this helps :)