Question

seja m(3,3) o ponto médio do segmento ab .calcule as coordenadas do ponto A sabendo que B (4.0)

Answer 1

Se $M(x_{_M}},\,y_{_{M}})$ é o ponto médio do segmento formado pelos pontos

$A(x_{_A},\,y_{_A})~\text{ e }~B(x_{_B},\,y_{_B}),$


então devemos ter

$\bullet\;\;x_{_M}=\dfrac{x_{_A}+x_{_B}}{2}\\\\\\ 2x_{_M}=x_{_A}+x_{_B}\\\\ x_{_A}=2x_{_M}-x_{_B}\\\\\\\\ \bullet\;\;y_{_M}=\dfrac{y_{_A}+y_{_B}}{2}\\\\\\ 2y_{_M}=y_{_A}+y_{_B}\\\\ y_{_A}=2y_{_M}-y_{_B}$

_______________

Para esta questão, temos

$M(3,\,3)~\text{ e }~B(4,\,0).$


e portanto,

$\bullet\;\;x_{_A}=2x_{_M}-x_{_B}\\\\ x_{_A}=2\cdot 3-4\\\\ x_{_A}=6-4\\\\ \boxed{\begin{array}{c}x_{_A}=2 \end{array}}\\\\\\ \bullet\;\;y_{_A}=2y_{_M}-y_{_B}\\\\ y_{_A}=2\cdot 3-0\\\\ \boxed{\begin{array}{c}y_{_A}=6 \end{array}}$


O ponto é $A(2,\,6).$