Answer :
Answer: The required center of the circle is (1, 2).
Step-by-step explanation: Given that the diameter of a circle has endpoints whose coordinates are r(-2, 2) and s(4, 2).
We are to find the center of the circle.
We know that
the center of a circle always lies in the middle of every diameter of the circle.
So, the co-ordinates of the midpoint of the diameter will be the center of the circle.
Now, the co-ordinates of the midpoint of a line segment with endpoints (a, b) and (c, d) is given by
[tex]M=\left(\dfrac{a+c}{2},\dfrac{b+d}{2}\right).[/tex]
Therefore, the co-ordinates of the midpoint of the diameter will be
[tex]M=\left(\dfrac{-2+4}{2},\dfrac{2+2}{2}\right)=\left(\dfrac{2}{2},\dfrac{4}{2}\right)=(1,2).[/tex]
Thus, the required center of the circle is (1, 2).