Question

The endpoints of the diameter of a circle are (2, 2) and (-4,-2). Sketch the circle. a. What are the coordinates of the center of the circle? b. What is the measure of the radius of the circle? c. Find the area and circumference of the circle to the nearest tenth.

Answer 1

a.

b. Let's find the diameter using the distance formula:

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

Where:

(x1,y1) = (2,2)

(x2,y2) = (-4,-2)

$\begin{gathered} d=\sqrt[]{(-4-2)^2+(-2-2)^2} \\ d=\sqrt[]{(-6)^2+(-4)^2} \\ d=\sqrt[]{52} \\ d=2\sqrt[]{13}\approx7.2111 \end{gathered}$

The radius of the circle is the diameter of the circle divided by 2:

$r=\frac{d}{2}=\sqrt[]{13}\approx3.6$

c. The area is given by:

$A=\pi\cdot r^2=\pi\cdot(\sqrt[]{13})^2=\pi\cdot13\approx40.8$

And the circumference is given by:

$C=2\cdot\pi\cdot r=2\cdot\pi\cdot\sqrt[]{13}\approx22.6$