To determine whether the point (2,2,1) lies on the graph of the equation x²+y²+z²=9, you have to substitute the coordinates of the point into the equation.
The x, y, and z coordinates of the point are 2, 2, and 1 respectively.
We will start by squaring each of these coordinates:
x² = 2² = 4,
y² = 2² = 4,
z² = 1² = 1.
Next, we will add these squares together (x²+y²+z²) which means we add the results we got from each of the squared coordinates:
4 (from x²) + 4 (from y²) + 1 (from z²) = 9.
We find that when we substitute the point (2,2,1) into our equation, the left-hand-side (LHS) of the equation equals 9. The right-hand-side of our equation was already 9.
Since both sides of the equation are equal (that is, LHS equals RHS), we can conclude that the point (2,2,1) indeed lies on the graph of the equation x²+y²+z²=9.