The diameter of a circle with endpoints A(-1,5) and A(4,-3) Use the midpoint formula to find the coordinates of the center of circle P(xy).
the midpoint is at ((-1+4)/2,(5-3)/2) = (3/2,1)
(-1, 5), (x, y), (4, -3).
x - (-1) = 4 - x.
X = 3/2 = 1.5.
y - 5 = -3 - y.
Y = 1.
To find the coordinates of the center of circle P, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint between two points, (x1, y1) and (x2, y2), can be found by taking the average of the x-coordinates and the average of the y-coordinates.
In this case, the endpoints of the diameter of the circle are A(-1, 5) and A(4, -3). Let's label the coordinates of point A1 as (x1, y1) and the coordinates of point A2 as (x2, y2):
Point A1: (x1, y1) = (-1, 5)
Point A2: (x2, y2) = (4, -3)
Now, we can use the midpoint formula to find the coordinates of the center of circle P:
x-coordinate of P = (x1 + x2) / 2
y-coordinate of P = (y1 + y2) / 2
Plugging in the values:
x-coordinate of P = (-1 + 4) / 2 = 3 / 2 = 1.5
y-coordinate of P = (5 + (-3)) / 2 = 2 / 2 = 1
Therefore, the coordinates of the center of circle P are (1.5, 1).