Question

Find the area and perimeter of rectangle MATH whose endpoints are M(-3, 1), A(1, 3), T(2, 1), and

H(-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\\\\ M(\stackrel{x_1}{-3}~,~\stackrel{y_1}{1})\qquad A(\stackrel{x_2}{1}~,~\stackrel{y_2}{3}) ~\hfill MA=√((~~ 1- (-3)~~)^2 + (~~ 3- 1~~)^2) \\\\\\ ~\hfill MA=√(( 4 )^2 + ( 2)^2) \implies \boxed{MA=√( 20)}`

`A(\stackrel{x_1}{1}~,~\stackrel{y_1}{3})\qquad T(\stackrel{x_2}{2}~,~\stackrel{y_2}{1}) ~\hfill AT=√((~~ 2- 1~~)^2 + (~~ 1- 3 ~~)^2) \\\\\\ ~\hfill AT=√(( 1)^2 + ( -2)^2) \implies \boxed{AT=√( 5)} \\\\\\ T(\stackrel{x_1}{2}~,~\stackrel{y_1}{1})\qquad H(\stackrel{x_2}{-2}~,~\stackrel{y_2}{-1}) ~\hfill TH=√((~~ -2- 2~~)^2 + (~~ -1- 1~~)^2) \\\\\\ ~\hfill TH=√(( -4)^2 + ( -2)^2) \implies \boxed{TH=√( 20)}`

`H(\stackrel{x_1}{-2}~,~\stackrel{y_1}{-1})\qquad M(\stackrel{x_2}{-3}~,~\stackrel{y_2}{1}) ~\hfill HM=√((~~ -3- (-2)~~)^2 + (~~ 1- (-1)~~)^2) \\\\\\ ~\hfill HM=√(( -1)^2 + ( 2)^2) \implies \boxed{HM=√( 5)} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\LARGE Perimeter}}{√(20)+√(5)+√(20)+√(5)}\implies ~~ \approx ~~ \text{\LARGE 13.42}`