### Instruction: Three vertices of a cube in space have coordinates $A = (2,3,0),$ $B = (0,5,4),$ and $C = (4,1,8).$  Compute the coordinates of the center of the cube.### Response: I need to find the coordinates of the point $O$ that is the center of the cube.
One way to do that is to find the midpoint of the diagonal $AC,$ since that will also be the center of the cube.
To find the midpoint of a line segment, I can use the formula: $(x_1 + x_2)/2, (y_1 + y_2)/2, (z_1 + z_2)/2.$
Plugging in the coordinates of $A$ and $C,$ I get: $(2 + 4)/2, (3 + 1)/2, (0 + 8)/2.$
Simplifying, I get: $3, 2, 4.$