, 2023

Suppose we call the unknown vertex $V$. The side of the rectangle joining the points $(2,1)$ and $(2,5)$ is vertical, and so the opposite side of the rectangle (the side joining $(4,1)$ to $V$) must also be vertical. This means that $V$ has the same $x$-coordinate as $(4,1)$, which is 4. Similarly, the side of the rectangle joining the points $(2,1)$ and $(4,1)$ is horizontal, and so the opposite side of the rectangle (the side joining $(2,5)$ to $V$) must also be horizontal. This means that $V$ has the same $y$-coordinate as $(2,5)$, which is 5. Therefore, the coordinates of the fourth vertex of the rectangle are $(4,5)$.