Question

Find the circumference and area of a circle with the diameter AB, A(-8,4) and B(4,-1)

Answer 1

$\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{-8}~,~\stackrel{y_1}{4})\qquad B(\stackrel{x_2}{4}~,~\stackrel{y_2}{-1})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ AB=\sqrt{[4-(-8)]^2+[-1-4]^2}\implies AB=\sqrt{(4+8)^2+(-1-4)^2} \\\\\\ AB=\sqrt{144+25}\implies AB=\sqrt{169}\implies \stackrel{\textit{diameter}}{AB=13}~\hfill \boxed{\stackrel{\textit{radius}}{6.5}} \\\\[-0.35em] ~\dotfill$

$\bf \textit{circumference of a circle}\\\\ C=2\pi r\qquad \qquad C=2\pi (6.5)\implies C=13\pi \implies C\approx 40.84 \\\\\\ \textit{area of a circle}\\\\ A=\pi r^2\qquad \qquad A=\pi (6.5)^2\implies A=42.25\pi \implies A\approx 132.73$