Question

Find the perimeter of rectangle BCEF. (0,3) (4,-1) (2,-3) (-2,1)

Answer 1

`~\hfill \stackrel{\textit{\large distance between 2 points}}{d = √(( x_2- x_1)^2 + ( y_2- y_1)^2)}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ B(\stackrel{x_1}{0}~,~\stackrel{y_1}{3})\qquad C(\stackrel{x_2}{4}~,~\stackrel{y_2}{-1}) ~\hfill BC=√((~~ 4- 0~~)^2 + (~~ -1- 3~~)^2) \\\\\\ ~\hfill BC=√(( 4 )^2 + ( -4)^2)\implies \boxed{BC=√(32)}`

`C(\stackrel{x_1}{4}~,~\stackrel{y_1}{-1})\qquad E(\stackrel{x_2}{2}~,~\stackrel{y_2}{-3}) ~\hfill CE=√((~~ 2- 4~~)^2 + (~~ -3- (-1) ~~)^2) \\\\\\ ~\hfill CE=√(( -2)^2 + ( -2)^2)\implies \boxed{CE=√(8)} \\\\\\ E(\stackrel{x_1}{2}~,~\stackrel{y_1}{-3})\qquad F(\stackrel{x_2}{-2}~,~\stackrel{y_2}{1}) ~\hfill EF=√((~~ -2- 2~~)^2 + (~~ 1- (-3)~~)^2) \\\\\\ ~\hfill EF=√(( -4)^2 + ( 4)^2)\implies \boxed{EF=√(32)}`

`F(\stackrel{x_1}{-2}~,~\stackrel{y_1}{1})\qquad B(\stackrel{x_2}{0}~,~\stackrel{y_2}{3}) ~\hfill FB=√((~~ 0- (-2)~~)^2 + (~~ 3- 1~~)^2) \\\\\\ ~\hfill FB=√(( 2)^2 + ( 2)^2)\implies \boxed{FB=√(8)} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\LARGE Perimeter} }{√(32)+√(8)+√(32)+√(8) ~~ \approx ~~ \text{\LARGE 16.97}}`