Question

Sendo M (5, 4) o ponto médio do segmento AB com A (x, y) e B (3, 4). Calcule as coordenadas de A.

Answer 1

$\boxed{\begin{array}{l}\underline{\rm Ponto\,m\acute edio\,de\,um\,segmento}\\\tt Dados\,os\,pontos\,A( x_A,y_A)\,e\,B(x_B,y_B)\\\tt De~\!\!fine-se\,ponto\,m\acute edio\,de\,A\,e\,B\\\tt O\,ponto\,M(x_M,y_M)~tal~que\\\tt x_M=\dfrac{x_A+x_B}{2}\,~e~y_M=\dfrac{y_A+y_B}{2}\end{array}}$

$\boxed{\begin{array}{l}\rm dados:\begin{cases}\tt M(5,4)\longrightarrow x_M=5~e~y_M=4\\\tt B(3,4)\longrightarrow x_B=3~e~y_B=4\\\tt A(x,y)\longrightarrow x_A=?~~y_A=? \end{cases}\\\underline{\bf soluc_{\!\!,}\tilde ao\!:}\\\tt x_M=\dfrac{x_A+x_B}{2}\implies x_A=2x_M-x_B\\\\\tt x_A=2\cdot5-3\\\tt x_A=10-3\\\tt x_A=7\\\tt y_M=\dfrac{y_A+y_B}{2}\implies y_A=2y_M-y_B\\\\\tt y_A=2\cdot4-4\\\tt y_A=8-4\\\tt y_A=4\end{array}}$

$\huge\boxed{\boxed{\boxed{\boxed{\tt A(7,4)\blue{\maltese}~\red{\mathbb{D}\mathbb{E}\mathbb{U}\mathbb{S}~\mathbb{V}\mathbb{U}\mathbb{L}\mathbb{T}}}}}}$