Question

What is the perimeter of a triangle with the points (-9,4) (7,4) and (7, -8)

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\\\\ A(\stackrel{x_1}{-9}~,~\stackrel{y_1}{4})\qquad B(\stackrel{x_2}{7}~,~\stackrel{y_2}{4}) ~\hfill AB=√((~~ 7- (-9)~~)^2 + (~~ 4- 4~~)^2) \\\\\\ ~\hfill AB=√(( 16)^2 + ( 0)^2)\implies \boxed{AB=16} \\\\\\ B(\stackrel{x_1}{7}~,~\stackrel{y_1}{4})\qquad C(\stackrel{x_2}{7}~,~\stackrel{y_2}{-8}) ~\hfill BC=√((~~ 7- 7~~)^2 + (~~ -8- 4~~)^2)`

`~\hfill BC=√(( 0)^2 + ( -12)^2)\implies \boxed{BC=12} \\\\\\ C(\stackrel{x_1}{7}~,~\stackrel{y_1}{-8})\qquad A(\stackrel{x_2}{-9}~,~\stackrel{y_2}{4}) ~\hfill CA=√((~~ -9- 7~~)^2 + (~~ 4- (-8)~~)^2) \\\\\\ ~\hfill CA=√(( -16)^2 + (12)^2)\implies CA=√(400)\implies \boxed{CA=20} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{Perimeter}{16~~ + ~~12~~ + ~~20\implies \text{\LARGE 48}}`