One end of the diameter of a circle is A(4,1) and its centre is C(3,3). The coordinates of the other end of the diameter is

Coordinate of one end of diameter of circle = \$(4, 1)\$ and centre of circle = \$(3, 3)\$.

Let (x, y) be the other end of the diameter of circle.

We know that centre of circle is the mid-point of diameter(longest chord) of circle.
Therefore,

\$(\frac{x + 4}{2}, \frac{y + 1}{2} ) = (3, 3) \$

Equating coordinates.

\begin{align} \frac{x + 4}{2} &= 3, & \frac{y + 1}{2} &= 3 \\ x + 4 &= 6, & y + 1 &= 6 \\ x &= 2, & y &= 5 \\ \end{align}

Answer

The other end of diameter of circle is \$ (2,5) \$