Question

Obtenha as coordenadas do ponto médio do segmento AB nos seguintes casos:
a) A(3, 1) e B(-3, 5)

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

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

d) A(b + 2, b) e B(6 - b, 5b)

Answer 1

Boa tarde Vitoria!

Solução!

Para obtermos as coordenadas do ponto médio vamos usar essa formula.


$m=\left ( \dfrac{x_{A}-x_{B} }{2}, \left \dfrac{ y_{A}+y_{B} }{2} \right \right )$

a)

$A(3,1)\\\\B(-3,5)$

Vamos agora substituir os pontos na formula.

$m=\left ( \dfrac{3-3 }{2}, \left \dfrac{ 1+5 }{2} \right \right )$

$m=(0,3)$



b)

$A\left ( \dfrac{5}{3},6\right )\\\\\\ B\left ( -\dfrac{2}{3},1\right )$


$m=\left ( \dfrac{5 }{3}- \left \dfrac{2}{3},\left \dfrac{6+1}{2}\right )$


$m=\left (\left \dfrac{1}{2} \right ,\left \dfrac{7}{2} \right )$



c)

$A(0,4)\\\\ B( -\frac{3}{4},0)$


$m=\left (0- \left \dfrac{3 }{8},\left \dfrac{4+0}{2}\right)$


$m=\left (- \left \dfrac{3 }{8},2 \right )$


d)

$A(b+2,b) \\\\\ B(6-b,5b)$


$m=\left ( \dfrac{b+2+6-b }{2}, \left \dfrac{ b+5b }{2} \right \right )$


$m=\left ( \dfrac{2+6 }{2}, \left \dfrac{ 6b }{2} \right \right )$


$m=(4,3b)$


Boa tarde!
Bons estudos!