MATH SOLVE

4 months ago

Q:
# 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?

Accepted Solution

A:

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)