Question

The endpoints of a regular pentagon are (-1,4) and (2,3). What is the perimeter of the Pentagon?

1. Square root of 10
2. 5 square root of 10
3. 5 square root of 2
4. 25 square root of 2

Answer 1

the assumption being that the endpoints are two continuous points in the pentagon, Check picture below.

`\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-1}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{3})\qquad \qquad d = √(( x_2- x_1)^2 + ( y_2- y_1)^2) \\\\\\ d=√([2-(-1)]^2+[3-4]^2)\implies d=√((2+1)^2+(3-4)^2) \\\\\\ d=√(9+1)\implies d=√(10)~\hfill \stackrel{\stackrel{~\hfill \stackrel{\textit{5 sides}}{}}{\textit{perimeter of the pentagon}}}{5√(10)}`