Question

01. Construa o plano cartesiano, localize os pontos e determine no caderno o
ponto médio do segmento de reta de extremidades A e B nos itens a seguir.
a) A(3, 4) e B(2,- 6)
b) A(-8, 3) e B17,-3)​

Answer 1

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Ponto médio de um segmento

$\large\boxed{\begin{array}{l}\sf Dado~os~pontos~A(x_A,y_A)~e~B(x_B,y_B)~chamamos\\\sf de~ponto~m\acute edio~do~segmento~AB ~o~ponto\\\sf M(x_M,y_M)~ onde\\\huge \boxed{\boxed{\boxed{\boxed{\sf x_M=\dfrac{x_A+x_B}{2}}}}}~\rm e~\boxed{\boxed{\boxed{\boxed{\sf y_M= \dfrac{y_A+y_B}{2}}}}}\end{array}}$

$\tt a)~\sf A(3, 4)~B(2,-6)\\\sf x_M=\dfrac{x_A+x_B}{2}\\\sf x_M=\dfrac{3+2}{2}\\\sf x_M=\dfrac{5}{2}\\\sf y_M=\dfrac{y_A+y_B}{2}\\\sf y_M=\dfrac{4-6}{2}\\\sf y_M=-\dfrac{2}{2}\\\sf y_M=-1\\\huge\boxed{\boxed{\boxed{\boxed{\sf M\bigg(\dfrac{5}{2},-1\bigg)}}}}\checkmark$

$\tt b)~\sf A(-8,3)~B(17,-3)\\\sf x_M=\dfrac{-8+17}{2}=\dfrac{9}{2}\\\sf y_M=\dfrac{y_A+y_B}{2}\\\sf y_M=\dfrac{3-3}{2}=0\\\huge\boxed{\boxed{\boxed{\boxed{\sf M\bigg(\dfrac{9}{2},0\bigg)}}}}\checkmark$