Question

A circle is drawn on a coordinate plane so that the endpoints of a diameter are located on points (-1,4) and (7,2). What is the area of the circle?

Answer 1

1. Find the distance from (-1,4) to (7,2) using the distance formula
2. The radius of your circle is 1/2 of that distance
3. Area = Pi * radius^2

Answer 2

\(\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
&({\color{red}{ -1}}\quad ,&{\color{blue}{ 4}})\quad &({\color{red}{ 7}}\quad ,&{\color{blue}{ 2}})
\end{array}\qquad
diameter = \sqrt{({\color{red}{ x_2}}-{\color{red}{ x_1}})^2 + ({\color{blue}{ y_2}}-{\color{blue}{ y_1}})^2}
\\ \quad \\
\textit{area of a circle}=\pi r^2\qquad \qquad r=\frac{diameter}{2}\)