Question

check
find circumference and area
round to nearest tenth if
necessary.
find r: $sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$

Explanation:

Step1: Calculate the radius

The distance formula between two points $A(x_1,y_1)=(2,2)$ and $B(x_2,y_2)=(5,5)$ is $r = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Substitute the values: $r=\sqrt{(5 - 2)^2+(5 - 2)^2}=\sqrt{3^2+3^2}=\sqrt{9 + 9}=\sqrt{18}=3\sqrt{2}$.

Step2: Calculate the circumference

The formula for the circumference of a circle is $C = 2\pi r$. Substitute $r = 3\sqrt{2}$ into the formula: $C=2\pi\times3\sqrt{2}=6\sqrt{2}\pi$.

Step3: Calculate the area

The formula for the area of a circle is $A=\pi r^{2}$. Substitute $r = 3\sqrt{2}$ into the formula: $A=\pi\times(3\sqrt{2})^{2}=\pi\times18 = 18\pi$.

Answer:

Circumference: $6\sqrt{2}\pi$
Area: $18\pi$