Question

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

Answer 1

C (2, -3) is the center 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

$\to$ 2 = $\frac{a+1}{2}$

$\to$ 4 = a+1

$\to$ a = 4 -1

$\to$ a = 3

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

$\to$ -6 = b + 4

$\to$ b = – 6 - 4

$\to$ b = -10

Therefore, the coordinates of point A are (3,-10)