So the slope/gradient will be in unknown as C(x,y) ?
A(-1,4) and B(7,5)
Slope of AC = (y-4)/(x+1)
Slope of BC = (y-5)/(x-7)
They are perpendicular because ACB is a right angled triangle.So
(y-4)(y-5)/(x+1)(x-7) = -1.
After simplification you will get the locus of C.