Question

Calcule as coordenadas do ponto M(ponto médio) do segmento AB, sendo:
a) A(-1,4) e B(5,2)
b) A/3,-1) e B(-2,1)
c) A(1,7) e B(11,3)
d) A(-2,5) e B(-4,-1)​

Answer 1

Explicação:

a)

• $\sf x_M=\dfrac{x_{A}+x_{B}}{2}$

$\sf x_M=\dfrac{-1+5}{2}$

$\sf x_M=\dfrac{4}{2}$

$\sf \red{x_M=2}$

• $\sf y_M=\dfrac{y_{A}+y_{B}}{2}$

$\sf y_M=\dfrac{4+2}{2}$

$\sf y_M=\dfrac{6}{2}$

$\sf \red{y_M=3}$

Logo, $\sf \red{M(2,3)}$

b)

• $\sf x_M=\dfrac{x_{A}+x_{B}}{2}$

$\sf x_M=\dfrac{3-2}{2}$

$\sf \red{x_M=\dfrac{1}{2}}$

• $\sf y_M=\dfrac{y_{A}+y_{B}}{2}$

$\sf y_M=\dfrac{-1+1}{2}$

$\sf y_M=\dfrac{0}{2}$

$\sf \red{y_M=0}$

Logo, $\sf \red{M\Big(\dfrac{1}{2},0\Big)}$

c)

• $\sf x_M=\dfrac{x_{A}+x_{B}}{2}$

$\sf x_M=\dfrac{1+11}{2}$

$\sf x_M=\dfrac{12}{2}$

$\sf \red{x_M=6}$

• $\sf y_M=\dfrac{y_{A}+y_{B}}{2}$

$\sf y_M=\dfrac{7+3}{2}$

$\sf y_M=\dfrac{10}{2}$

$\sf \red{y_M=5}$

Logo, $\sf \red{M(6,5)}$

d)

• $\sf x_M=\dfrac{x_{A}+x_{B}}{2}$

$\sf x_M=\dfrac{-2-4}{2}$

$\sf x_M=\dfrac{-6}{2}$

$\sf \red{x_M=-3}$

• $\sf y_M=\dfrac{y_{A}+y_{B}}{2}$

$\sf y_M=\dfrac{5-1}{2}$

$\sf y_M=\dfrac{4}{2}$

$\sf \red{y_M=2}$

Logo, $\sf \red{M(-3,2)}$