Question

Por favor me ajudem
Dado um segmento de reta AB cujas extremidades estão nas coordenadas A = (0; 6) e B = (4; – 10), então a coordenada do seu ponto médio é?

a) M=(–3; –1,5)

b) M=( 2; – 2)

c) M=(3; -2)

d)M= (-2; 0)

e) M = (2; – 1)

Answer 1

$\large\boxed{\begin{array}{l}\sf Sejam~A(x_A,y_A)~B(x_B,y_B)\\\sf dois~pontos~quaisquer~do~plano~cartesiano.\\\sf o~ponto~m\acute edio~de~A~e~B~\acute e~o~ponto~M(x_M,y_M)\\\sf onde~x_M=\dfrac{x_A+x_B}{2}~e~y_M=\dfrac{y_A+y_B}{2}\end{array}}$

$\large\boxed{\begin{array}{l}\sf A(0,6)~B(4,-10)\\\sf x_A=0~y_A=6~~x_B=4~~y_B=-10\\\sf x_M=\dfrac{x_A+x_B}{2}\\\sf x_M=\dfrac{0+4}{2}\\\sf x_M=\dfrac{4}{2}\\\sf x_M=2\\\sf y_M=\dfrac{y_A+y_B}{2}\\\sf y_M=\dfrac{6+(-10)}{2}\\\sf y_M=\dfrac{6-10}{2}\\\sf y_M=-\dfrac{4}{2}\\\sf y_M=-2\\\sf M(2,-2)\\\huge\boxed{\boxed{\boxed{\boxed{\sf\maltese~alternativa~b}}}}\end{array}}$