Question

AB is a diameter of a circle with centre 0. If the ooordinates of A and 0 are ( 1, 4) and (3, 6 ). Find the ooordinates of B and the length of the diameter. 

Answer 1

O is the centre of the circle with diameter AB .

∴ AO : OB = 1 : 1

Coordinnates of O are ,

O (3 , 6) = O `((1 + "x")/2 , (4 + "y")/2)`

`3 = (1 + "x")/2   , 6 = (4 + "y")/2`

6 = 1 + x   ,    12 = 4 + y

x = 5 , y = 8

Coordinates of B are (5 , 8)

Length of AB = `sqrt ((5 - 1)^2 + (8 - 4)^2)`

`= sqrt (16 + 16) = 4 sqrt 2` units