Question

The endpoints of CD are C(–8, 4) and D(6, –6). What are the coordinates of point P on CD such that P is the length of the line segment from D? (–2.75, 0.25) (–5, 2.5) (0.75, –2.25) (3.75, –3.75)

Answer 1

If you graph the end points C and D then graph the 4 points at the end it is difficult to tell which points are on CD without a line.  
Using the endpoints find the slope (change in y/ change in x) then substitute a point in to find the intercept.  
Slope = (-6-4)/(6- -8) = -5/7
Intercept equation (-6) = -5/7 (6) + b
b = -1.71428571429
Graphing the line shows only 2 points on the line (–2.75, 0.25) and (0.75, –2.25)
I am confused by the part, "P is the length of the line segment from D".  Were you given a length P to help you determine which point.  Using the distance formula to find the length from each point to D doesn't help determine which one is best with the information you have given.  The image shows the distances I calculated and the graphed points. 
I hope this helps!

Answer 2

the answer is (–2.75, 0.25). hope this helps :)