Question

Find the coordinates of a point $A$, where $AB$ is the diameter of a circle whose centre is $(2,-3)$ and $B$ is $(1,4)$.

Answer 1

Let the coordinates of $A$ be $(x,y)$

$AB$ is a diameter of the circle then Midpoint of $AB$ is center of the circle which is $(2,-3$)

Mid point of A and B$=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

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

$\Rightarrow \frac{x+1}{2}=2$

$\Rightarrow x+1=4\Rightarrow x=3$

$\Rightarrow \frac{y+4}{2}=-3$

$\Rightarrow y+4=-6$

$\Rightarrow y=-10$

$\therefore$Coordinates of $A$ is $(3,-10)$.