One end of the diameter of a circle is (6,9) and the centre is (0,0). Find the co-ordinate of the other end of the diameter.

Coordinate of one end of diameter of circle = \$(6,9)\$ and centre of circle = \$(0,0)\$.

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 + 6}{2}, \frac{y + 9}{2}) = 0 \$

Equating coordinates.

\begin{align} \frac{x + 6}{2} &= 0, & \frac{y + 9}{2} &= 0 \\ x + 6 &= 0, & y + 9 &= 0 \\ x&= -6, & y &= -9 \\ \end{align}

Answer

The other end of diameter of circle is \$(−6,−9)\$.