To determine if a point lies on a circle, we can use the standard equation of a circle, which is (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius. In this case, the center is (-3, 1) and the radius is 4, so the equation becomes (x + 3)^2 + (y - 1)^2 = 16 (since 4^2 = 16). We then substitute the coordinates of the point (-1, 4) into the left side of the equation: (-1 + 3)^2 + (4 - 1)^2 = 2^2 + 3^2 = 4 + 9 = 13. Since 13 is not equal to 16, the point (-1, 4) does not lie on the circle.