Question

A distância entre os pontos M(-1,-7) e N (4,5 ) do plano Xoy vale:
A) 14
B) - 13
C) 12
D) 9
E) 13

Answer 1

⠀

⠀⠀☞ A distância entre os pontos M e N é de 13 (opção E). ✅

⠀

⠀

⚡ " -Como encontramos a distância entre dois pontos no plano cartesiano?"

⠀

⠀

                $\setlength{\unitlength}{0.95cm}\begin{picture}(6,5)\thicklines\put(0,0){\vector(1,0){5}}\put(0,0){\vector(0,1){5}}\put(0,0){\vector(-1,0){5}}\put(0,0){\vector(0,-1){5}}\put(4.8,0.2){x}\put(0.2,4.8){y}\put(-3,-1){\line(5,3){5}}\put(-3,-1){\circle*{0.13}}\put(2,2){\circle*{0.13}}\put(2,-1){\circle*{0.13}}\bezier{20}(2,2)(2,0.5)(2,-1)\bezier{35}(-3,-1)(-0.5,-1)(2,-1)\put(-3.7,-1){\LARGE \sf A }\put(1.5,2.1){\LARGE \sf B }\put(2.3,0.4){\Large \sf \Delta y }\put(-1,-1.6){\Large \sf \Delta x }\put(-1.5,1){\Large \sf d_{AB} }\put(1,-4){\dashbox{0.1}(5.5,1.5){\text{\Large \sf d_{AB}^2 = (\Delta x)^2 + (\Delta y)^2 }}}\end{picture}$

⠀

⠀

                            $\Large\red{\boxed{\begin{array}{rcl}&\green{\underline{\footnotesize\sf Esta~imagem~n\tilde{a}o~\acute{e}~visualiz\acute{a}vel~pelo~App~Brainly.}}&\\&\green{\footnotesize\sf \bullet~Experimente~compartilhar\rightarrow copiar~e~acessar}&\\&\green{\footnotesize\sf o~link~copiado~pelo~seu~navegador~ou~Browser.}&\\\end{array}}}$

⠀

⠀

⠀⠀⠀➡️⠀Através do Teorema de Pitágoras:

⠀

⠀

                             $\large\red{\boxed{\pink{\boxed{\begin{array}{rcl}&&\\&\orange{\sf d_{AB} = \sqrt[2]{\sf \Delta x^2 + \Delta y^2}}&\\&&\\&\Downarrow~~~~~~~~~~\Downarrow&\\&&\\&\orange{\sf d_{AB} = \sqrt[2]{\sf (x_B - x_A)^2 + (y_B - y_A)^2}}&\\&&\\\end{array}}}}}$

⠀

⠀

$\text{\pink{ \Longrightarrow }~\Large\orange{ \sf d_{AB} }}$ sendo a distância entre os pontos A e B;

$\text{\pink{ \Longrightarrow }~\Large\orange{ \sf (x_A, y_A) }}$ sendo as coordenadas do ponto A;

$\text{\pink{ \Longrightarrow }~\Large\orange{ \sf (x_B, y_B) }}$ sendo as coordenadas do ponto B;

⠀

⠀

⠀⠀⠀➡️⠀Temos que a distância será sempre uma grandeza positiva. Desta forma temos:

⠀

$\large\blue{\sf d_{MN} = \sqrt{(4 - (-1))^2 + (5 - (-7))^2}}$

⠀

$\LARGE\blue{\sf d_{MN} = \sqrt{5^2 + 12^2}}$

⠀

$\LARGE\blue{\sf d_{MN} = \sqrt{25 + 144}}$

⠀

$\LARGE\blue{\sf d_{MN} = \sqrt{169}}$

⠀

$\LARGE\blue{\sf d_{MN} = 13}$  

⠀

⭐ O que nos leva à opção E). ✌

⠀

⠀

                                           $\Huge\green{\boxed{\rm~~~\red{E)}~\blue{ 13 }~~~}}$ ✅

⠀

⠀

⠀

⠀

                             $\bf\large\red{\underline{\quad\quad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}$☁

⠀

⠀⠀☀️ L͎̙͖͉̥̳͖̭̟͊̀̏͒͑̓͊͗̋̈́ͅeia mais sobre distância entre dois pontos:

⠀

                                     https://brainly.com.br/tarefa/38357197 ✈  

                                     https://brainly.com.br/tarefa/47174094 ✈  

⠀

⠀

⠀

                                     $\huge\blue{\text{\bf\quad Bons~estudos.}}$⠀☕

⠀

                                          $\quad\qquad(\orange{D\acute{u}vidas\ nos\ coment\acute{a}rios})$ ☄

⠀

                             $\bf\large\red{\underline{\qquad \qquad \qquad \qquad \qquad \qquad \quad }\LaTeX}$✍

                                $\sf(\purple{+}~\red{cores}~\blue{com}~\pink{o}~\orange{App}~\green{Brainly}$ ☘☀❄☃☂☻)

⠀

⠀

⠀

⠀

                                                          $\Huge\green{\text{ \underline{\red{\mathbb{S}}\blue{\mathfrak{oli}}~}~\underline{\red{\mathbb{D}}\blue{\mathfrak{eo}}~}~\underline{\red{\mathbb{G}}\blue{\mathfrak{loria}}~} }}$ ✞

⠀

Answer 2

Explicação passo-a-passo:

M(-1,-7) e N (4,5 )

M(-1 e -7)

xa=-1

ya=-7

N (4,5 )

xb=4

yb=5

$d = \sqrt{(xa - xb) {}^{2} + (ya - yb) {}^{2} }$

$d = \sqrt{( - 1 - 4) {}^{2} + ( - 7 - 5) {}^{2} }$

$d = \sqrt{( - 5) {}^{2} + ( - 12) {}^{2} }$

$d = \sqrt{25 + 144}$

$d = \sqrt{169}$

$d = 13u.$

(Opção "E")