Question

Determinar o simétrico de A(3,8) em relação ao ponto P(-2,1)?

Answer 1

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$\large\begin{array}{l} \textsf{S\~ao dados os pontos}\\\\ \mathsf{A(3,\,8)~~e~~P(-2,\,1).} \\\\\\\textsf{De acordo com o enunciado da tarefa, deseja-se encontrar}\\\textsf{as coordenadas do ponto }\mathsf{B(x_{_B},\,y_{_B}),}\textsf{ de modo que} \end{array}$


•   $\large\begin{array}{l} \mathsf{P(-2,\,1)}\textsf{ \'e o ponto m\'edio do segmento }\overline{\mathsf{AB}}: \end{array}$

$\large\begin{array}{l} \mathsf{x_{_P}=\dfrac{x_{_A}+x_{_B}}{2}}\\\\ \mathsf{2x_{_P}=x_{_A}+x_{_B}}\\\\ \mathsf{x_{_B}=2x_{_P}-x_{_A}}\\\\ \mathsf{x_{_B}=2\cdot (-2)-3}\end{array}$

$\large\begin{array}{l} \mathsf{x_{_B}=-4-3}\\\\ \mathsf{x_{_B}=-7\qquad\quad\checkmark}\\\\\\ \mathsf{y_{_P}=\dfrac{y_{_A}+y_{_B}}{2}}\\\\ \mathsf{2y_{_P}=y_{_A}+y_{_B}} \end{array}$

$\large\begin{array}{l} \mathsf{y_{_B}=2y_{_P}-y_{_A}}\\\\ \mathsf{y_{_B}=2\cdot 1-8}\\\\ \mathsf{y_{_B}=2-8}\\\\ \mathsf{y_{_B}=-6\qquad\quad\checkmark} \end{array}$


$\large\begin{array}{l} \textsf{O ponto procurado \'e o ponto }\mathsf{B(-7,\,-6).}\\\\\\\\ \textsf{Bons estudos! :-)} \end{array}$


Tags:  simétrico ponto médio simetria geometria analítica