Question

find the circumference and area of circle x if each unit on the graph measures 1 centimeter. round answers to the nearest tenth, if necessary. x(-3,4) y(-4,2) circumference cm area cm²

Explanation:

Step1: Calculate the radius

The distance between the center $X(-3,4)$ and a point on the circle $Y(-4,2)$ is the radius. Use the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here $x_1=-3,y_1 = 4,x_2=-4,y_2 = 2$. So $r=\sqrt{(-4 + 3)^2+(2 - 4)^2}=\sqrt{(-1)^2+(-2)^2}=\sqrt{1 + 4}=\sqrt{5}$.

Step2: Calculate the circumference

The formula for the circumference of a circle is $C = 2\pi r$. Substitute $r=\sqrt{5}$ into it, $C=2\pi\sqrt{5}\approx2\times3.14\times2.24\approx14.0$.

Step3: Calculate the area

The formula for the area of a circle is $A=\pi r^{2}$. Substitute $r = \sqrt{5}$ into it, $A=\pi\times(\sqrt{5})^{2}=5\pi\approx5\times3.14 = 15.7$.

Answer:

circumference: $14.0$ cm
area: $15.7$ $cm^{2}$