What are the coordinates of the center of a circle if the endpoints of its diameter are A(3,-2) and B (7,1) -
a. Substitute into the equation of a circle (x - h) + ( - k) = 7
To find the coordinates of the center of the circle, we first need to find the midpoint of the diameter AB, which will be the center of the circle.
The midpoint formula for two points A(x1, y1) and B(x2, y2) is:
Midpoint = ( (x1 + x2) / 2 , (y1 + y2) / 2 )
In this case, the endpoints of the diameter are A(3, -2) and B(7, 1):
Midpoint = ( (3 + 7) / 2 , (-2 + 1) / 2 )
Midpoint = (10 / 2 , -1 / 2 )
Midpoint = (5, -0.5)
Therefore, the center of the circle is at point (5, -0.5).
Now, substitute these values into the equation of a circle:
(x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius.
(x - 5)^2 + (y - (-0.5))^2 = 7
The equation of the circle with the given diameter and center is:
(x - 5)^2 + (y + 0.5)^2 = 7