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

(-5,-3)

Explanation:

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Answer 2

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

Explanation:

* Lets explain how to solve the problem

- The mid-point of the segment whose endpoints are (x1 , y1) , (x2 , y2)

is
`((x_(1)+x_(2))/(2),(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=(-9+-1)/(2)=(-10)/(2)=-5`

∴
`y=(-1+-5)/(2)=(-6)/(2)=-3`

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

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