a diameter of a circle has endpoints (-9,5) and (5,5)
Find the center of the circle using th midpoint formula
find the radius you can use the distance formula with an endpoint of the diameter and the center
write an equation for the circle
1. Finding the center of the circle using the midpoint formula:
Let the coordinates of the center of the circle be (h, k).
The midpoint formula is:
Midpoint = ((x1 + x2)/2, (y1 + y2)/2)
Plugging in the coordinates of the endpoints of the diameter:
Midpoint = ((-9 + 5)/2, (5 + 5)/2)
Midpoint = ((-4)/2, (10)/2)
Midpoint = (-2, 5)
Therefore, the center of the circle is (-2, 5).
2. Finding the radius using the distance formula:
Let's use one endpoint of the diameter, (-9, 5), and the center, (-2, 5), to find the radius.
The distance formula is:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Plugging in the coordinates:
Distance = √((-2 + 9)^2 + (5 - 5)^2)
Distance = √(7^2 + 0)
Distance = √49
Distance = 7
Therefore, the radius of the circle is 7.
3. Writing an equation for the circle:
The general equation of a circle is:
(x - h)^2 + (y - k)^2 = r^2
Plugging in the values we found:
(x + 2)^2 + (y - 5)^2 = 7^2
(x + 2)^2 + (y - 5)^2 = 49
So, the equation of the circle is:
(x + 2)^2 + (y - 5)^2 = 49