Question

The poimt 3,-4 is the centre of a circle if AB is a diameter of the circle and B is 5,6 find the coordinate of A

Answer 1

Given :

Consider the coordinates of A(x, y).

Coordinates of the centre of the circle O(3, -4).

B(5, 6).

AO = OB ( Radius of circle )

therefore O is a midpoint of AB.

ratio of AO : OB are 1:1.

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

O (3, -4) = [(x+5)/2 , (y+6)/2]

3 = (x+5)/2 -4 = (y+6)/2

6 = x+5. -8 = y+6

x = 1. y= -14

Therefore, the coordinates of A(1, -14).

Answer 2

full answer with diagram