Question

the circumference of the circle is about select choice units and its area is about select choice square units. q(-2, 2) p(3, -2)

Explanation:

Step1: Find the radius using distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Let the center of the circle be $P(3,-2)$ and a point on the circle be $Q(-2,2)$. Then $r=\sqrt{(3 + 2)^2+(-2 - 2)^2}=\sqrt{25 + 16}=\sqrt{41}\approx6.4$.

Step2: Calculate the circumference

The formula for the circumference of a circle is $C = 2\pi r$. Substituting $r\approx6.4$, we get $C=2\pi\times6.4\approx2\times3.14\times6.4 = 40.192\approx40.2$.

Step3: Calculate the area

The formula for the area of a circle is $A=\pi r^{2}$. Substituting $r\approx6.4$, we get $A = \pi\times(6.4)^{2}\approx3.14\times40.96=128.6144\approx128.6$.

Answer:

The circumference of the circle is about $40.2$ units and its area is about $128.6$ square units.