Given:
The coordinates of the point A and B are (-5,-1) and (4,1)
The point P on the directed line segment from A to B such that P is One-fourth the length of the line segment from A to B.
Thus, we have;
and

We need to determine the coordinates of the point P(x,y)
x - coordinates of the point P:
The x - coordinates of the point P can be determined using the formula,

Substituting the values, we get;



Thus, the x - coordinate of the point P is

y - coordinate of the point P:
The y - coordinate of the point P can be determined using the formula,

Substituting the values, we get;




Thus, the y - coordinate of the point P is

Therefore, the coordinates of the point P is

Hence, Option C is the correct answer.