A rectangle has its vertices at the following coordinates: \(A(1, 2)\), \(B(1, 5)\), \(C(4, 5)\), and \(D(4, 2)\). What are the coordinates of the center of the rectangle?

To find the center of the rectangle with vertices \(A(1, 2)\), \(B(1, 5)\), \(C(4, 5)\), and \(D(4, 2)\), we can use the midpoint formula for one of the diagonals. The diagonals of a rectangle bisect each other, so the center will be the midpoint of either diagonal \(AC\) or \(BD\). Let's calculate the midpoint of diagonal \(AC\): 1. **Coordinates of \(A\)**: \((1, 2)\) 2. **Coordinates of \(C\)**: \((4, 5)\) The midpoint \(M\) is given by: \[ M = \left( \frac{x_A + x_C}{2}, \frac{y_A + y_C}{2} \right) = \left( \frac{1 + 4}{2}, \frac{2 + 5}{2} \right) = \left( \frac{5}{2}, \frac{7}{2} \right) \] So, the coordinates of the center of the rectangle are \(\left( \frac{5}{2}, \frac{7}{2} \right)\), which can also be written as \((2.5, 3.5)\). **Answer:** The center of the rectangle is ( 2.5, 3.5 ).