Draw vertical lines from the known, Q, and unknown, P, points to the x-axis:



There are two similar right triangles.  The line from the origin to Q(-5,-12)
is the hypotenuse of the large right triangle.  We find it by the Pythagorean
theorem








We want the hypotenuse of the smaller right triangle to be 1.
The line from the origin to P(x,y) is the hypotenuse of the small right
triangle, and we set it to equal 1.



or









or





 

---




or







So the coordinates of the point that is 1 unit along the line is

P(x,y) = 

Edwin