Question

Urgente: Determine as coordenadas do ponto médio dos segmentos AB
a) A(-1, 3) e B(4,-5)
b) A(-2/3, 4) e B(3,-1/3)​

Answer 1

Explicação passo-a-passo:

Para calcular o ponto médio entre dois pontos, utilizamos a seguinte fórmula:

$x_{m} =\dfrac{x_{a}+x_{b} }{2} \\\\y_{m} =\dfrac{y_{a}+y_{b} }{2}$

a)Temos que A(-1, 3) e B(4,-5).

$x_{m} =\dfrac{-1+4 }{2} \\\\x_{m} =\dfrac{3 }{2}$

$y_{m} =\dfrac{3+(-5) }{2} \\\\y_{m} =\dfrac{-2 }{2} \\\\y_{m}=-1$

$M\bigg(\dfrac{3}{2},-1\bigg)$

b)Temos que A(-2/3, 4) e B(3,-1/3)​.

$x_{m} =\dfrac{\frac{-2}{3} +3 }{2}\\\\x_{m} =\dfrac{\frac{-2}{3} +\frac{9}{3} }{2}\\\\x_{m} =\dfrac{\frac{7}{3} }{2}\\\\x_{m} =\dfrac{7 }{6}$

$y_{m} =\dfrac{4+\frac{-1}{3} }{2}\\\\y_{m} =\dfrac{\frac{12}{3} +\frac{-1}{3} }{2}\\\\y_{m} =\dfrac{\frac{11}{3} }{2}\\\\y_{m} =\dfrac{11 }{6}$

$M\bigg(\dfrac{7}{6},\ \dfrac{11}{6}\bigg)$