The equation of a circle can be found when you know the endpoints of its diameter.
To find the center of the circle, you take the average of the x-coordinates and the average of the y-coordinates of the endpoints of the diameter.
For this case:
Center = ((1-3)/2, (3+1)/2) = (-1, 2)
Then, you find the radius of the circle by calculating the distance between one endpoint of the diameter and the center using the distance formula.
Radius = √[(-3 - (-1))² + (1 - 2)²] = √[(-2)² + (-1)²] = √[4 + 1] = √5
Therefore, the equation of the circle with center (-1, 2) and radius √5 is:
(x + 1)² + (y - 2)² = 5
So, the correct answer is:
D. (x - 1)² + (y - 2)² = 5
