Question

Sendo P o ponto médio do segmento AB, onde P(6 , 3) e B(-1 , -2). Desta forma quais são as coordenadas de A?

Answer 1

$\large\boxed{\begin{array}{l}\underline{\sf D~\!\!efinic_{\!\!,}\tilde ao\,de\,ponto\,m\acute edio}\\\rm Dados\,os\,pontos\, A(x_A,y_A)~e~B(x_B,y_B)\\\rm d~\!\!efinimos\,como\,ponto\,m\acute edio\,de\,um\,segmento\\\rm o\,ponto\,M(x_M,y_M)~tal\,que\\\huge\boxed{\boxed{\boxed{\boxed{\rm x_M=\dfrac{x_A+x_B}{2}}}}}~\rm e~\huge\boxed{\boxed{\boxed{\boxed{\rm y_M=\dfrac{y_A+y_B}{2}}}}}\end{array}}$

$\large\boxed{\begin{array}{l}\rm P(6,3)~~~B(-1,-2)~~A(x_A,y_A).\\\rm x_P=\dfrac{ x_A+x_B}{2}\longrightarrow x_A=2x_P-x_B\\\\\rm x_A= 2\cdot6-(-1)\\\rm x_A=12+1\\\rm x_A=13\\\\\rm y_P=\dfrac{y_A+y_B}{2}\longrightarrow y_A=2y_P-y_B\\\\\rm y_A=2\cdot3-(-2)\\\rm y_A=6+2\\\rm y_A=8\\\rm A(13,8)\end{array}}$