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A point $(x_k,y_k)$ must be chosen because the subrectangle is a two-dimensional region, not a single input value. To determine the height of the representative box standing over that subrectangle, one must evaluate the function $f(x,y)$ at a specific location.

Conditions: The domain is partitioned into subrectangles.; A function $f(x,y)$ defines the surface height.

A point $(x_k,y_k)$ must be chosen because the subrectangle is a two-dimensional region, not a single input value. To determine the height of the representative box standing over that subrectangle, one must evaluate the function $f(x,y)$ at a specific location.

Conditions: The domain is partitioned into subrectangles.; A function $f(x,y)$ defines the surface height.