Answer:
The coordinates of the center of this circle are (-5 , -3)
Step-by-step explanation:
* Lets explain how to solve the problem
- The mid-point of the segment whose endpoints are (x1 , y1) , (x2 , y2)
is [tex](\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})[/tex]
- AB is the diameter of circle T
∵ The diameter must passing through the center of the circle
∵ The center of the circle is the mid-point of all diameters of the circle
∵ The center of the circle is point T
∴ T is the mid point of the diameter AB
- Lets calculate the coordinates of point T by using the rule above
∵ A = (-9 , -1) and B = (-1 , -5)
∵ T is the mid-point of AB
- Let A = (x1 , y1) , B = (x2 , y2) and T = (x , y)
∴ x1 = -9 , x2 = -1 and y1 = -1 , y2 = -5
∴ [tex]x=\frac{-9+-1}{2}=\frac{-10}{2}=-5[/tex]
∴ [tex]y=\frac{-1+-5}{2}=\frac{-6}{2}=-3[/tex]
∴ The coordinates of point T are (-5 , -3)
* The coordinates of the center of this circle are (-5 , -3)
