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).

Question

Philoid · Accepted Answer

Let the coordinates of A be × & y. So A(X,Y) and B(1,4)

2 = (m₁x₂ + m₂x₁)/ m₁ + m₂

2 = (1 × 1 + 1 × X)/1 + 1

2 = (1 + X) /2

1 + X = 4

× = 3

– 3 = (m₁y₂ + m₂y₁)/ m₁ + m₂

– 3 = (1× 4 + 1 × Y)/2

– 3 = (4 + Y)/2

(4 + Y) = – 6

Y = – 10

A(3, – 10)