Question

What is the perimeter of the polygon with these coordinates: (1,-2) (4,2) (6,2) and (9,-2)?

Answer 1

\(\textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({\color{red}{ 1}}\quad ,&{\color{blue}{ -2}})\quad
% (c,d)
&({\color{red}{ 4}}\quad ,&{\color{blue}{ 2}})
\\\hline\\
&({\color{red}{ 4}}\quad ,&{\color{blue}{ 2}})\quad
% (c,d)
&({\color{red}{ 6}}\quad ,&{\color{blue}{ 2}})
\\\hline\\
&({\color{red}{ 6}}\quad ,&{\color{blue}{ 2}})\quad
% (c,d)
&({\color{red}{ 9}}\quad ,&{\color{blue}{ -2}})
\\\hline\\
&({\color{red}{ 9}}\quad ,&{\color{blue}{ -2}})\quad
% (c,d)
&({\color{red}{ 1}}\quad ,&{\color{blue}{ -2}})
\end{array}\qquad
% distance value
d = \sqrt{({\color{red}{ x_2}}-{\color{red}{ x_1}})^2 + ({\color{blue}{ y_2}}-{\color{blue}{ y_1}})^2}\)
get the distance of each segment, add them up, that'd be the perimeter

Answer 2

20 units (unless there's a specific unit of measurement you're using)