Question

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

Explanation:

Step1: Calculate the radius

Use the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$ to find the radius $r$ between points $P(3,-2)$ and $Q(-2,2)$. Here $x_1 = 3,y_1=-2,x_2=-2,y_2 = 2$. Then $r=\sqrt{(-2 - 3)^2+(2+ 2)^2}=\sqrt{(-5)^2+4^2}=\sqrt{25 + 16}=\sqrt{41}\approx6.4$.

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 $A=\pi\times(6.4)^{2}=3.14\times40.96 = 128.6144\approx128.6$. But we focus on the circumference answer for the given - choice problem.

Answer:

The circumference of the circle is 40.2 units and its area (not in - choice here but for full - understanding) is approximately 128.6 square units. For the given choices, the circumference answer is 40.2.