The coords of the 4th vertex are (7,-12).
The diagram below shows why.
The vertices have been labelled A, B, C, D. The dotted triangles are congruent, and we know the side lengths. The horizontal distance between B and A is the difference between their x-coords=8-1=7. So we add 7 to the x-coord of C to get the x-coord of D, 7+0=7. The vertical distance between B and A is the difference between their y-coords=0-(-4)=4, vertically downwards. So we have to moved downwards the same distance from C to get to D, so we subtract 4 from -8 to get -12, the y-coord of D. So D is (7,-12). The grid squares help you to see what’s going on.