The centre of a circle is C(-2, 3) and one end of a diameter PQ is P(2, -4). Find the co-ordinates of Q.

Since PQ is the diameter of the circle and C is the center, C must be the mid-point of the segment PQ.

Let coordinates of Q be (x₁, y₁).

By using mid-point formula,

x-coordinate = $\Big(\dfrac{x$1 + x2}{2}\Big)

Substituting values we get :

$\Rightarrow -2 = \Big(\dfrac{2 + x$1}{2}\Big) \\[1em] \Rightarrow -4 = 2 + x1 \\[1em] \Rightarrow -4 - 2 = x1 \\[1em] \Rightarrow x1 = -6.

By using mid-point formula,

y-coordinate = $\Big(\dfrac{y$1 + y2}{2}\Big)

Substituting values we get :

$\Rightarrow 3 = \Big(\dfrac{-4 + y$1}{2}\Big) \\[1em] \Rightarrow 6 = -4 + y1 \\[1em] \Rightarrow 6 + 4 = y1 \\[1em] \Rightarrow y1 = 10.

Q = (x₁, y₁) = (-6, 10).

Hence, coordinates of Q are (-6, 10).