Distance from point (4,1,-1) to plane x-2y+2z+3 = 0 is 1.
The formula for the distance from a point to a plane is
d = abs(Ax + By + Cz + D) / sqrt(A^2 + B^2 + C^2)
where
d = distance
(x,y,z) = coordinates of point
A,B,C,D = coefficients of equation for the plane
For this problem, the values for A,B,C,and D are A=1, B=-2, C=2, and D=3. So substituting the known values into the equation, we get:
d = abs(1*x - 2*y + 2*z + 3) / sqrt(1^2 + (-2)^2 + 2^2)
d = abs(1*4 - 2*1 + 2*(-1) + 3) / sqrt(1 + 4 + 4)
d = abs(4 - 2 - 2 + 3) / sqrt(9)
d = abs(3) / 3
d = 1
