Question

AB¯¯¯¯¯¯¯¯ is the diameter of circle T. Point A is located at (-9,-1) and point B is located at (-1,-5). What are the coordinates of the center of this circle?

Answer 1

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 $(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})$

- 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

∴ $x=\frac{-9+-1}{2}=\frac{-10}{2}=-5$

∴ $y=\frac{-1+-5}{2}=\frac{-6}{2}=-3$

∴ The coordinates of point T are (-5 , -3)

* The coordinates of the center of this circle are (-5 , -3)