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

Let the coordinates of point A be (x, y).

Mid-point of AB is (2, - 3), which is the center of the circle.

According to the mid point formula,

O(x, y) = [(x₁ + x₂) / 2, (y₁ + y₂) / 2]

We have A(x, y) and B(1, 4) and the center is (2, -3)

Therefore by using midpoint formula,

(2, -3) = [(x + 1) / 2, (y + 4) / 2]

⇒ (x + 1) / 2 = 2 and (y + 4) / 2 = - 3 (By Cross multiplying & transposing)

⇒ x + 1 = 4 and y + 4 = - 6

⇒ x = 3 and y = - 10

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