Question

find the circumference and area of the figure 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

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

Step2: Calculate the circumference

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

Step3: Calculate the area

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

Answer:

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