The endpoints of a diameter of a circle are A(2,1) and B(5,5. Find the area of the circle in terms of pi.
the diameter is the distance between the two points: √((5-2)^2+(5-1)^2 = 5
Now it's a cinch, right?
A. 24/4 square units
To find the area of a circle, we need to know the radius. The radius can be found by finding the distance between the endpoints of the diameter.
Step 1: Find the length of the diameter AB using the distance formula.
Distance formula: d = √[(x2 - x1)^2 + (y2 - y1)^2]
d = √[(5 - 2)^2 + (5 - 1)^2]
= √[(3)^2 + (4)^2]
= √[9 + 16]
= √25
= 5
Step 2: Divide the length of the diameter by 2 to find the radius.
Radius (r) = Diameter (d) / 2
r = 5 / 2
= 2.5
Step 3: Use the formula for the area of a circle to calculate the area.
Area of a circle: A = πr^2
A = π(2.5)^2
= 6.25π
Therefore, the area of the circle is 6.25π (in terms of π).
To find the area of a circle using the given endpoints of a diameter, we can use the distance formula to determine the length of the diameter.
The distance formula is given by:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Let's calculate the distance between the points A(2,1) and B(5,5) to find the length of the diameter:
Diameter AB = √((5 - 2)^2 + (5 - 1)^2)
= √(3^2 + 4^2)
= √(9 + 16)
= √25
= 5
Now that we have the diameter, we can use it to calculate the radius, which is half the length of the diameter:
Radius = Diameter / 2
= 5 / 2
= 2.5
The formula for the area of a circle is:
Area = π * (radius)^2
Plugging in the value of the radius, we have:
Area = π * (2.5)^2
= π * 6.25
= 6.25π
Therefore, the area of the circle in terms of pi is 6.25π.