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?A. (-4, -2)B. (-2, -4)C. (-3, -5)D. (-5, -3)

Answer 1

D. (-5, -3)

Explanation:

We have that AB is the diameter of the circle T, we know that the diameter must pass through the center of the circle, also that the center of the circle is the midpoint of all the diameters of the circle, therefore, the midpoint of the diameter AB are the coordinates of the center of the circle.

The midpoint between two points can be calculated as follows:

`\begin{gathered} (x_m,y_m)=((x_1+x_2)/(2),(y_1+y_2)/(2)) \\ \text{replacing the point A (-9,-1) and point B (-1,-5)} \\ \text{replacing:} \\ (x_m,y_m)=((-9-1)/(2),\frac{-1-5_{}}{2}) \\ (x_m,y_m)=((-10)/(2),\frac{-6_{}}{2}) \\ (x_m,y_m)=(-5,-3) \end{gathered}`

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