Points A(3,5) and B(7,10) are the endpoints of a diameter of a circle graphed in a coordinate plane. How many square units are in the area of the circle? Express your answer in terms of pi.
figure the length of the diameter d, using your distance formula. Then the area of the circle is
A = πd^2/4
To find the area of the circle, we first need to find the radius of the circle. The radius is half the length of the diameter.
Step 1: Calculate the length of the diameter.
Using the distance formula, we can find the distance between points A(3, 5) and B(7, 10).
Distance = √((x2 - x1)² + (y2 - y1)²)
Distance = √((7 - 3)² + (10 - 5)²)
Distance = √(4² + 5²)
Distance = √(16 + 25)
Distance = √41
The length of the diameter is √41.
Step 2: Calculate the radius.
The radius is half the length of the diameter.
Radius = (√41) / 2
Step 3: Calculate the area of the circle.
The formula for the area of a circle is A = πr², where A is the area and r is the radius.
Area = π * (radius)²
Area = π * (√41/2)²
Area = π * (41/4)
Area = (41π)/4
Therefore, the area of the circle is (41π)/4 square units.