Question

The diameter of a circle has endpoints whose coordinates are r(-2, 2) and s(4, 2). find the center of the circle.

Answer 1

Therefore the coordinates of centre are (1,2)

Answer 2

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

`M=\left((a+c)/(2),(b+d)/(2)\right).`

Therefore, the co-ordinates of the midpoint of the diameter will be

`M=\left((-2+4)/(2),(2+2)/(2)\right)=\left((2)/(2),(4)/(2)\right)=(1,2).`

Thus, the required center of the circle is (1, 2).