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?

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To find the center of the rectangle with vertices at $$A(1, 2)$$, $$B(1, 5)$$, $$C(4, 5)$$, and $$D(4, 2)$$, we can calculate the midpoint of one of the diagonals.

Let's use the diagonal from $$A$$ to $$C$$:
- Coordinates of $$A$$: $$(1, 2)$$
- Coordinates of $$C$$: $$(4, 5)$$

The midpoint $$M$$ of diagonal $$AC$$ is calculated as:
$$
M = \left( \frac{1 + 4}{2}, \frac{2 + 5}{2} \right) = \left( \frac{5}{2}, \frac{7}{2} \right) = \left(2.5, 3.5\right)
$$

Alternatively, using the diagonal from $$B$$ to $$D$$:
- Coordinates of $$B$$: $$(1, 5)$$
- Coordinates of $$D$$: $$(4, 2)$$

The midpoint $$M$$ of diagonal $$BD$$ is also:
$$
M = \left( \frac{1 + 4}{2}, \frac{5 + 2}{2} \right) = \left( \frac{5}{2}, \frac{7}{2} \right) = \left(2.5, 3.5\right)
$$

Therefore, the coordinates of the center of the rectangle are:

$$\boxed{\left(\dfrac{5}{2},\ \dfrac{7}{2}\right)}$$
The center of the rectangle is at $$\left(2.5, 3.5\right)$$.

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?

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