Question

Determine as coordenadas do ponto médio do segmento AB,nos seguintes casos:
a) A(3,-2) e B(-1,-6)
b) A( -1,5) e B(5,-2)
c) A(-4,-2) e B(-2,-4)

Answer 1

Fórmula Geral de Ponto Médio: $( \frac{ x_{1} + x_{2} }{2} ; \frac{ y_{1} + y_{2} }{2} )$




$a) A(3,-2) e B(-1,-6)\\\\\\x= \frac{ 3+(-1)}{2} \to x= \frac{ 3-1 }{2} \to x= \frac{2}{2} \to x=1 \\\\\\ y=\frac{-2+(-6) }{2}\to y= \frac{-2-6}{2} \to y= \frac{ -8 }{2} \to y=-4\\ \\\\ PM=(1, -4)$




$b) A( -1,5) e B(5,-2)\\\\\\x= \frac{ -1+5}{2} \to x= \frac{4}{2} \to x=2 \\\\\\ y=\frac{5+(-2) }{2}\to y= \frac{5-2}{2} \to y= \frac{ 3 }{2} \\\\ PM=(2, \frac{ 3 }{2})$




$c) A(-4,-2) e B(-2,-4)\\\\\\x= \frac{ -4+(-2)}{2} \to x= \frac{ -4-2 }{2} \to x= \frac{-6}{2} \to x=-3 \\\\\\ y=\frac{-2+(-4) }{2}\to y= \frac{-2-4}{2} \to y= \frac{ -6 }{2} \to y=-3\\ \\\\ PM=(-3,-3)$



Espero ter ajudado, bons estudos...

Answer 2

M(AB) = (A+B)/2
a)
M = ([3+(-1)]/2, [-2+(-6)]/2) = (2/2, -8/2) = (1,-4)
M(AB)=(1,-4)

b)
M(AB)=((-1+5)/2, [5+(-2)]/2) = (4/2,3/2) = (2 , 1.5)

c)
M(AB) = ([(-4+(-2)]/2, [-2+(-4)]/2) = (-6/2,-6/2) = (-3,-3)