Question

Determine o ponto simétrico de (2, -3) em relação a (5, $\frac{1}{2}$)

Answer 1

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$\large\begin{array}{l} \textsf{S\~ao dados os pontos}\\\\ \mathsf{A(2,\,-3)~~e~~P(5,\,\frac{1}{2}).} \\\\\textsf{De acordo com o enunciado da tarefa, deseja-se encontrar}\\\textsf{as coordenadas do ponto }\mathsf{B(x_{_B},\,y_{_B}),}\textsf{ de modo que} \end{array}$


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

$\large\begin{array}{l} \mathsf{x_{_P}=\dfrac{x_{_A}+x_{_B}}{2}}\\\\ \mathsf{2x_{_P}=x_{_A}+x_{_B}}\\\\ \mathsf{x_{_B}=2x_{_P}-x_{_A}}\\\\ \mathsf{x_{_B}=2\cdot 5-2}\end{array}$

$\large\begin{array}{l} \mathsf{x_{_B}=10-2}\\\\ \mathsf{x_{_B}=8\qquad\quad\checkmark}\\\\\\ \mathsf{y_{_P}=\dfrac{y_{_A}+y_{_B}}{2}}\\\\ \mathsf{2y_{_P}=y_{_A}+y_{_B}} \end{array}$

$\large\begin{array}{l} \mathsf{y_{_B}=2y_{_P}-y_{_A}}\\\\ \mathsf{y_{_B}=2\cdot \dfrac{1}{2}-(-3)}\\\\ \mathsf{y_{_B}=1+3}\\\\ \mathsf{y_{_B}=4\qquad\quad\checkmark} \end{array}$


$\large\begin{array}{l} \textsf{O ponto procurado \'e o ponto }\mathsf{B(8,\,4).}\\\\\\ \textsf{D\'uvidas? Comente.}\\\\\\ \textsf{Bons estudos! :-)} \end{array}$


Tags:  simétrico ponto médio simetria geometria analítica