Question

1- Dados os pontos A (2,2) e B (5,6), determine:
a) A distância entre eles;
b) As coordenadas do ponto médio entre eles.

Answer 1

Resposta:

a) 5. b) (3,5; 4)

Explicação passo-a-passo:

a) Distância

d^2 = (5 - 2)^2 + (6 - 2)^2

d^2 = 3^2 + 4^2

d^2 = 9 + 16

d = √25

d = 5

b) Ponto médio

x = (2 + 5)/2

x = 7/2

x = 3,5

y = (2 + 6)/2

y = 8/2

y = 4

Answer 2

$\Large\displaystyle\text{ \begin{gathered} \sf{\sf{d_{AB }=\sqrt{(x_{A} -x_{B})^{2}+(y_{A} -y_{B})^{2}}} } \end{gathered} }$

$\Large\displaystyle\text{ \begin{gathered} \sf{ d_{AB}=\sqrt{(5-2)^2+(6-2)^2}} \end{gathered} }$

$\Large\displaystyle\text{ \begin{gathered} \sf{ d_{AB}=\sqrt{3^2+4^2} }\end{gathered} }$

$\Large\displaystyle\text{ \begin{gathered} \sf{ d_{AB}=\sqrt{9+16}} \end{gathered} }$

$\Large\displaystyle\text{ \begin{gathered} \sf{ d_{AB}=\sqrt{25}} \end{gathered} }$

$\Large\displaystyle\text{ \begin{gathered} \therefore\green{\underline{\boxed{\sf{d_{AB}= 5} }}}~~(\checkmark).\end{gathered} }$

$\Large\displaystyle\text{ \begin{gathered} \sf{ P_m=\bigg(\dfrac{x_A+x_B}{2},\dfrac{y_A+y_B}{2}\bigg)} \end{gathered} }$

$\Large\displaystyle\text{ \begin{gathered} \sf{P_m=\bigg(\dfrac{2+5}{2},\dfrac{2+6}{2}\bigg) } \end{gathered} }$

$\Large\displaystyle\text{ \begin{gathered} \sf{ P_m=\bigg(\dfrac{7}{2},\dfrac{8}{2}\bigg)} \end{gathered} }$

$\Large\displaystyle\text{ \begin{gathered} \green{\underline{\boxed{\sf{ P_m=(3{,}5;4)}}}}~~(\checkmark) .\end{gathered} }$