Question

Find the circumference of the given circle

Answer 1

$\huge\boxed{2\pi\sqrt{41}}$

Hey! Start by finding the radius. We will assume that point $P$ is the center point of the circle, so the radius is the distance between points $P$ and $Q$.

Let's use the distance formula, substituting in the known values:

$\begin{aligned}r&=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\&=\sqrt{(-2-3)^2+(2-(-2))^2}\end{aligned}$

Simplify:

$\begin{aligned}r&=\sqrt{(-2-3)^2+(2-(-2))^2}\\&=\sqrt{(-5)^2+4^2}\\&=\sqrt{25+16}\\&=\sqrt{41}\end{aligned}$

Now, we'll use the formula for the circumference of a circle, substituting in the known value:

$\begin{aligned}C&=2\pi r\\&=\boxed{2\pi\sqrt{41}}\\&\approx40.232\end{aligned}$

Answer 2

Answer:

40.21

Step-by-step explanation:

The circumference of a circle is 2πr; where are is the radius.  The radius is not given but two points

(x1,y1) = (-2,2)

(x2,y2) = (3,-2)

With the two points you can use the distance formula which will be equal to the radius

r = $\sqrt{(y2-y1)^{2} + (x2-x1)^{2} }$

r = $\sqrt{(-2-2)^{2} + (3+2)^{2} }$

r = $\sqrt{(-4)^{2} + (5)^{2} }$

r = $\sqrt{41 }$ = 6.40

circumference = 2πr = 2π(6.40) = 40.21