Question

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 .

Answer 1

The centre C is the mid-point of the diameter PQ.

So if $$Q(a, b)$$

$$\frac{2 + a}{2} = -2$$

$$\Rightarrow 2 + a = -4$$

$$\Rightarrow a=-6$$

$$\frac{-4 + b}{2} = 3$$

$$\Rightarrow -4 + b = 6$$

$$\Rightarrow b = 10$$

Hence the co-ordinates of Q are $$Q(-6, 10)$$.