Chapter 9 - Further Applications of the Integral and Taylor Polynomials - 9.3 Center of Mass - Preliminary Questions - Page 483: 4

See the explanation below.

Because a rectangle is symmetric with respect to both the vertical line and the horizontal line through the center of the rectangle, the Symmetry Principle guarantees that the centroid of the rectangle must lie along both of these lines. The only point in common to both lines of symmetry is the center of the rectangle, so the centroid of the rectangle must be the center of the rectangle.