What are the coordinates of the center of the circle that passes through the points (1, 1), (1, 5), and (5, 5)?A. (0, 0)B. (5, 1)C. (3, 3)D. (2.5, 2.5)
Accepted Solution
A:
Let the
location of the center (x,y)
let the
distance between center and point (5,5) = d₁
let the
distance between center and point (1,5) = d₂
let the
distance between center and point (1,1) = d₃
The
condition of the circle is d₁
= d₂ = d₃
Making
two equations to find x , y
d₁² = d₂²
∴
(x-5)²
+ (y-5)²
= (x-1)²
+ (y-5)²
∴
(x-5)² = (x-1)²
∴
x-5 = \pm (x-1) ⇒⇒⇒
positive sign unacceptable
∴
x-5 = -(x-1)
∴
x = 3
d₁² = d₃²
∴
(x-5)²
+ (y-5)²
= (x-1)²
+ (y-1)²
substituting
with x and simplifying the equation
∴
y = 3
∴center
= (3,3)
The correct choice will be (C) Answer ⇒⇒⇒ C. (3, 3)