Question:
Find the coordinates of a point A, where AB is the diameter of a circle with centre C(2, −3) and the other end of the diameter is B(1, 4).
Solution:
C(2, −3) is the centre of the given circle. Let A(a, b) and B(1, 4) be the two end-points of the given diameter AB. Then, the coordinates of C are
$x=\frac{a+1}{2}, y=\frac{b+4}{2}$
It is given that $x=2$ and $y=-3$.
$\Rightarrow 2=\frac{a+1}{2},-3=\frac{b+4}{2}$
$\Rightarrow 4=a+1,-6=b+4$
$\Rightarrow a=4-1, b=-6-4$
$\Rightarrow a=3, b=-10$
Therefore, the coordinates of point A are (3, -10).
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