AOD is a diameter of circle O. The coordinates of points A and D are (-11,-5)and (-3,-5)Find the area of circle O.
a. 9 pi
b. 16 pi
c. 25 pi
d. 64 pi
e. 116 pi
please answer and explain
just figure the distance between the points. That is the length of the diameter. Half of that is the radius.
Now figure the area of the circle.
16 pi
To find the area of a circle, we need to know the radius of the circle.
In this case, AOD is a diameter of the circle. The length of a diameter is equal to twice the length of the radius.
To find the length of the diameter AOD, we can use the distance formula between points A and D on the coordinate plane.
Let's calculate the length of the diameter AOD:
Distance between two points (x1, y1) and (x2, y2) is given by the formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Using the distance formula, we have:
d = sqrt((-3 - -11)^2 + (-5 - -5)^2)
= sqrt((8)^2 + (0)^2)
= sqrt(64)
= 8
So the length of the diameter AOD is 8 units.
Now, we can find the radius by dividing the length of the diameter by 2:
Radius = Diameter/2 = 8/2 = 4 units.
The area of a circle is given by the formula:
Area = π * r^2
Substituting the value of the radius into the formula, we get:
Area = π * (4)^2
= π * 16
Therefore, the area of circle O is 16π.
So the correct option is b. 16π.