Question

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

Answer 1

8.1240384 UNITS

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 = √(( 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=√((~~ -2- (-1)~~)^2 + (~~ 3- 1~~)^2) \\\\\\ ~\hfill AB=√(( -1)^2 + ( 2)^2) \implies \boxed{AB=√( 5 )}`

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

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