Question

1) Determine as coordenadas do ponto médio do segmento AB, quando:

a) A(1,7) e B(11, 3)

 b) A(- 2, 5) e B(-4, -1)

c) A(3, -1) e B(-2, 1)

 d) A(1/2, 1) e b(5/4, -4)

URGENTE!!!​

Answer 1

Explicação passo-a-passo:

As coordenadas do ponto médio são dadas por:

• $\sf x_M=\dfrac{x_A+x_B}{2}$

• $\sf y_M=\dfrac{y_A+y_B}{2}$

a)

• $\sf x_M=\dfrac{x_A+x_B}{2}$

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

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

$\sf x_M=6$

• $\sf y_M=\dfrac{y_A+y_B}{2}$

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

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

$\sf y_M=5$

O ponto médio é $\sf M(6,5)$

b)

• $\sf x_M=\dfrac{x_A+x_B}{2}$

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

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

$\sf x_M=-3$

• $\sf y_M=\dfrac{y_A+y_B}{2}$

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

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

$\sf y_M=2$

O ponto médio é $\sf M(-3,2)$

c)

• $\sf x_M=\dfrac{x_A+x_B}{2}$

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

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

• $\sf y_M=\dfrac{y_A+y_B}{2}$

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

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

$\sf y_M=0$

O ponto médio é $\sf M\left(\dfrac{1}{2},0\right)$

d)

• $\sf x_M=\dfrac{x_A+x_B}{2}$

$\sf x_M=\dfrac{\frac{1}{2}+\frac{5}{4}}{2}$

$\sf x_M=\dfrac{\frac{2+5}{4}}{2}$

$\sf x_M=\dfrac{\frac{7}{4}}{2}$

$\sf x_M=\dfrac{7}{4}\cdot\dfrac{1}{2}$

$\sf x_M=\dfrac{7}{8}$

• $\sf y_M=\dfrac{y_A+y_B}{2}$

$\sf y_M=\dfrac{1-4}{2}$

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

O ponto médio é $\sf M\left(\dfrac{7}{8},\dfrac{-3}{2}\right)$