Strong Work so far! I will use your results to proceed:
The didstance between the 2 given pionts is sqrt 20
set up a circle centered at -1, -1 with radius sqrt 20
(x+1)^2 + (y+1)^2 = r^2 = 20
to find the point(s) on the given perpindicular line, sub in y = -2x+2 into the circle equation
(x+1)^2 + (-2x+2 + 1)^2 = 20 expand and simplify to get
5x^2 - 10x -10 = 0 Quadratic fomula gives x = 1 +- sqrt(3) use these values to sub into the perpindicular line equation to find the correspondine 'y' values ....