Question

Se (2,3) é ponto médio de AB, com A(n,5) e B(4,m), quanto vale m+n+5?

Answer 1

$A(x_A,y_A)=A(n,5)\\ B(x_B,y_B)=(4,m)\\\\ \boxed{M_{AB}=(x_M,y_M)=M_{AB}\bigg(\dfrac{x_A+x_B}{2},\dfrac{y_A+y_B}{2}\bigg)}$

$x_M=2\ \therefore\ \dfrac{x_A+x_B}{2}=2\ \therefore\ n+4=4\ \therefore\ \boxed{n=0}\\\\ y_M=3\ \therefore\ \dfrac{y_A+y_B}{2}=3\ \therefore\ 5+m=6\ \therefore\ \boxed{m=1}\\\\ m+n+5=1+0+5\ \therefore\ \boxed{m+n+5=6}$