You are looking for the coordinates of a point on the line PQ with P(-9,3) and Q(-1,-7) whose distance from P (or Q) is of the whole length PQ.

All your calculations are OK. But:

If the line is determined by P and Q then (-5,-2) is the midpoint.

If the line is determined by P and Q then the distance of (-3,-9/2) to P is of the total length.

If the line is determined byQ and Pthen the distance of (-7, 1/2)to Qis of the total length.