Question

A (-1, 1), B (-2, 3), and C (3, 5). Find the perimeter of the triangle

Answer 1

Answer:

8.1240384 UNITS

Step-by-step explanation:

A (-1, 1), B (-2, 3), and C (3, 5)   =   AC = SQRT (16 + 16) =  SQRT 32      AB = SQRT 1 +4 =  SQRT 5    BC  =  SQRT 25 + 4 = SQRT 29   Perimeter = SQRT  32+ 5 + 29 = SQRT 66 = 8.1240384 UNITS

Answer 2

$~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ A(\stackrel{x_1}{-1}~,~\stackrel{y_1}{1})\qquad B(\stackrel{x_2}{-2}~,~\stackrel{y_2}{3}) ~\hfill AB=\sqrt{(~~ -2- (-1)~~)^2 + (~~ 3- 1~~)^2} \\\\\\ ~\hfill AB=\sqrt{( -1)^2 + ( 2)^2} \implies \boxed{AB=\sqrt{ 5 }}$

$B(\stackrel{x_1}{-2}~,~\stackrel{y_1}{3})\qquad C(\stackrel{x_2}{3}~,~\stackrel{y_2}{5}) ~\hfill BC=\sqrt{(~~ 3- (-2)~~)^2 + (~~ 5- 3~~)^2} \\\\\\ ~\hfill BC=\sqrt{( 5)^2 + ( 2)^2} \implies \boxed{BC=\sqrt{ 29 }}$

$C(\stackrel{x_1}{3}~,~\stackrel{y_1}{5})\qquad A(\stackrel{x_2}{-1}~,~\stackrel{y_2}{1}) ~\hfill CA=\sqrt{(~~ -1- 3~~)^2 + (~~ 1- 5~~)^2} \\\\\\ ~\hfill CA=\sqrt{( -4)^2 + (-4)^2} \implies \boxed{CA=\sqrt{ 32 }} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\LARGE perimeter}}{\sqrt{5}~~ + ~~\sqrt{29}~~ + ~~\sqrt{32} ~~ \approx ~~ \text{\LARGE 13.28}}$