Find the center and the radius of the circle which (6,-2) and (-4,4)are endpoints of a diameter.
Please help!
first, the diameter: use the distance formula.
second, the center: xcenter= 6+-4 /2=2
ycenter= -2+4 /2= 1
So for the diameter I got 136. This that right?
To find the center and radius of a circle when you have the endpoints of a diameter, you can use the midpoint formula to find the center and the distance formula to find the radius.
First, let's find the midpoint of the diameter. The midpoint formula is given by:
Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)
Let (x1, y1) = (6, -2) and (x2, y2) = (-4, 4).
Midpoint = ((6 + (-4)) / 2, (-2 + 4) / 2)
= (2/2, 2/2)
= (1, 1)
So, the midpoint is (1, 1).
The center of the circle is the same as the midpoint of the diameter, so the center of the circle is (1, 1).
Next, let's find the radius of the circle. The distance formula is given by:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Let (x1, y1) = (6, -2) and (x2, y2) = (-4, 4).
Distance = √((-4 - 6)^2 + (4 - (-2))^2)
= √((-10)^2 + (6)^2)
= √(100 + 36)
= √136
So, the radius of the circle is √136.
Therefore, the center of the circle is (1, 1) and the radius is √136.