Ponto médio

Nota: Não confundir com Ponto mediano.

O **ponto médio** do segmento de reta (x₁, y₁) até (x₂, y₂).

O ponto médio é o ponto de equilíbrio de um segmento de reta.^[1]

Podemos definir o ponto médio como o ponto que divide o segmento de reta exatamente no meio tendo dois segmentos iguais.

A fórmula para determinar o ponto médio de um segmento de reta num plano, com os pontos finais $(x_{1},y_{1})$ e $(x_{2},y_{2})$ é:

\left({\tfrac {x_{1}+x_{2}}{2}},{\tfrac {y_{1}+y_{2}}{2}}\right).

No espaço cartesiano de três dimensões, a fórmula do ponto médio é:

M=\left({\tfrac {x_{1}+x_{2}}{2}},{\tfrac {y_{1}+y_{2}}{2}},{\tfrac {z_{1}+z_{2}}{2}}\right).

Construção geométrica

Com o compasso centrado no ponto A, traçamos um arco com o raio igual à medida do segmento AB;

Com o compasso centrado no ponto B, traçamos um outro arco com o mesmo raio que antes;

Os arcos terão interseção em dois pontos localizados fora do segmento AB;

Traçamos a reta ligando os pontos obtidos na interseção dos arcos;

O ponto médio M é a interseção da reta com o segmento AB.

Referências

↑ Wolfram. «Midpoint» (em inglês). A Wolfram Web Resource. Consultado em 1 de agosto de 2014

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