Question

The endpoints of a diameter of a circle are (-3,-2) and (11,-10). What are the coordinates of the center of the circle?

Answer 1

Given:

The endpoints of a diameter of a circle are (-3,-2) and (11,-10).

The objective is to find the coordinates of the center of the circle.

Step-by-step explanation:

Consider the given coordinates as

`\begin{gathered} (x_1,y_1)=(-3,-2) \\ (x_2,y_2)=(11,-10) \end{gathered}`

The center of the circle must be the midpoint of the diameter of the circle.

Since the coordinates of diameter are given, the midpoint of the coordinates can be calculated as,

`(x,y)=((x_1+x_2)/(2),(y_1+y_2)/(2))\text{ . . . . .(1)}`

On plugging the given coordinates in equation (1),

`\begin{gathered} (x,y)=((-3+11)/(2),(-2+(-10))/(2)) \\ =((8)/(2),(-12)/(2)) \\ =(4,-6) \end{gathered}`

Hence, the coordinates of the center of the circle is (4,-6).