Question

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

Answer 1

Given:-

A circle with centre $(2,-3)$ and $AB$ is the diameter of circle with $B(1,4)$.

To find:- Coordinate of point $A$.

Let $(x,y)$ be the coordinate of $A$.

Since $AB$ is the diameter of the circle, the centre will be the mid-point of $AB$.

now, as centre is the mid-point of $AB$.

$x$-coordinate of centre $=\frac{x+1}{2}$

$y$-coordinate of centre $=\frac{y+4}{2}$

But given that centre of circle is $(2,-3)$.

Therefore,

$\frac{x+1}{2}=2\Rightarrow x=3$

$\frac{y+4}{2}=-3\Rightarrow y=-10$

Thus the coordinate of $A$ is $(3,-10)$.

Hence the correct answer is $(3,-10)$.