The endpoints of a diameter of a circle are (-1, 5) and (5, -3). What is the area of the circle?
Correct: B
First, find the center of the circle, which is the midpoint of the diameter.
Midpoint M = ((x1 + x2)/2, (y1 + y2)/2)
M = ((-1 + 5)/2, (5 + (-3))/2) = (4/2, 2/2) = (2, 1).
Next, find the radius. The radius is the distance from the center to one of the endpoints. Let's use (5, -3).
Radius r = sqrt((5 - 2)^2 + (-3 - 1)^2)
r = sqrt((3)^2 + (-4)^2)
r = sqrt(9 + 16)
r = sqrt(25)
r = 5
Finally, calculate the area of the circle, A = πr^2.
A = π(5)^2 = 25π.