AB is a diameter of a circle with centre (3, 4). If coordinates of A is the point (4, 9), then find the coordinates of B.
Answer & explanation
Correct answer: option 2
AB is a diameter of a circle with centre (3, 4).
Coordinates of A is the point (4, 9)
Assume C to be the centre of circle.
AC = sqrt((4-3)^2 + (9-4)^2) = sqrt(1+25) = sqrt(26)
Also AC = BC
Let B be at (x,y)
BC = sqrt((x-3)^2 + (y-4)^2) = sqrt(26)
(x-3)^2 + (y-4)^2 = 26
Applying hit and trial using the given options
(2-3)^2 + (-1-4)^2 = 26
1 + 25 = 26 (The condition is satisfiying the equation)
The correct answer is Option (2) → (2, -1)