Question

Find the circumference of circle a if each unit on the graph measures 1 centimeter

Answer 1

we know the center of the circle is at (2 , 3) and we also know the circle passes through (4 , 1), let's get that distance between those two points in order to get its radius.

`~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{2}~,~\stackrel{y_1}{3})\qquad B(\stackrel{x_2}{4}~,~\stackrel{y_2}{1})\qquad \qquad d = √(( x_2- x_1)^2 + ( y_2- y_1)^2) \\\\\\ AB=√((~~4 - 2~~)^2 + (~~1 - 3~~)^2)\implies AB=√( (2)^2 + (-2)^2) \\\\\\ AB=√( 4 + 4)\implies AB=√( 8 ) \\\\[-0.35em] ~\dotfill`

`\textit{Circumference of a Circle}\\\\ C=2\pi r ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=√(8) \end{cases}\implies C=2\pi √(8)\implies C\approx 17.77~cm^2`