Question

obtenha as coordenadas do ponto médio do segmento AB nos seguintes casos:

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Answer 1

Resposta:

a) (0, 3)

b) (1/2, 7/2)

c) (3/8, 2)

d) (4, 3)

Explicação passo a passo:

a) A(3, 1) e B(-3, 5)

$x_{A}=3 \\\\y_{A}=1 \\\\x_{B}=(-3) \\\\y_{B}=5 \\\\\\x_{M} =\frac{x_{A}+x_{B}}{2} \\\\ x_{M} =\frac{3+(-3)}{2} \\\\ x_{M} =\frac{3-3}{2} \\\\ x_{M} =\frac{0}{2} \\\\ x_{M} =0 \\\\\\ y_{M}=\frac{y_{A}+y_{B}}{2} \\\\ y_{M}=\frac{1+5}{2} \\\\ y_{M}=\frac{6}{2} \\\\ y_{M}=3 \\\\\\ \bold{P_{M} =(0, 3)}$

b) A(5/3, 6) e B(-2/3, 1)

$x_{A}=\frac{5}{3} \\\\y_{A}=6 \\\\x_{B}=\frac{-2}{3} \\\\y_{B}=1 \\\\\\x_{M} =\frac{x_{A}+x_{B}}{2} \\\\ x_{M} =\frac{\frac{5}{3}+\frac{-2}{3}}{2} \\\\ x_{M} =\frac{\frac{5-2}{3} }{2} \\\\ x_{M} =\frac{\frac{3}{3} }{2} \\\\x_{M} =\frac{1}{2} \\\\\\ y_{M}=\frac{y_{A}+y_{B}}{2} \\\\ y_{M}=\frac{6+1}{2} \\\\ y_{M}=\frac{7}{2} \\\\\\ \bold{P_{M} =(\frac{1}{2}, \frac{7}{2})}$

c) A(0, 4) e B(3/4, 0)

$x_{A}=0 \\\\y_{A}=4 \\\\x_{B}=\frac{3}{4} \\\\y_{B}=0 \\\\\\x_{M} =\frac{x_{A}+x_{B}}{2} \\\\ x_{M} =\frac{0+\frac{3}{4} }{2} \\\\ x_{M} =\frac{\frac{3}{4} }{2} \\\\ x_{M} =\frac{3}{4(2)} \\\\ x_{M} =\frac{3}{8} \\\\\\ y_{M}=\frac{y_{A}+y_{B}}{2} \\\\ y_{M}=\frac{4+0}{2} \\\\ y_{M}=\frac{4}{2} \\\\ y_{M}=2 \\\\\\ \bold{P_{M} =(\frac{3}{8} , 2)}$

d) A(2, 1) e B(6, 5)

$x_{A}=2 \\\\y_{A}=1 \\\\x_{B}=6 \\\\y_{B}=5 \\\\\\x_{M} =\frac{x_{A}+x_{B}}{2} \\\\ x_{M} =\frac{2+6}{2} \\\\ x_{M} =\frac{8}{2} \\\\ x_{M} =4 \\\\\\ y_{M}=\frac{y_{A}+y_{B}}{2} \\\\ y_{M}=\frac{1+5}{2} \\\\ y_{M}=\frac{6}{2} \\\\ y_{M}=3 \\\\\\ \bold{P_{M} =(4, 3)}$