Question

Considere "a" um número real e maior que 1. Se M (1, 3) é o ponto médio do segmento de reta de extremidades A (a, 4) e B (-2, 2), então o valor de "a" é:

A) 2
B) 3
C) 4
D) 5
E) Nenhuma das respostas anteriores

Answer 1

$\large\boxed{\begin{array}{l}\underline{\sf Ponto\,m\acute edio\,de\,um\,segmento}\\\rm dados\,os\,pontos\,A(x_A,y_A)\,e\,B(x_B,y_B)\\\rm de~\!\!finimos\,ponto\,m\acute edio\,de\,um\,segmento\\\rm o\,ponto\,M(x_M,y_M)~tal\,que\\\rm x_M=\dfrac{x_A+x_B}{2}~~e~y_M=\dfrac{y_A+y_B}{2}\end{array}}$

$\large\boxed{\begin{array}{l}\rm A(a,4 )~~B(-2,2)~~M(1,3)\\\\\rm x_M=\dfrac{x_A+x_B}{2}\\\\\rm 1=\dfrac{a-2}{2}\\\\\rm a-2=2\\\rm a=2+2\\\rm a=4\\\huge\boxed{\boxed{\boxed{\boxed{\rm\dagger\red{\maltese}~\blue{alternativa~C}}}}}\end{array}}$