Question

Agora, calcule a distância entre os pontos dos itens a seguir:
a. A(-1, 2) e B(5,2).
b. A(4, 1) e B(4, -3).
C. A(2, 3) e B(5, 1).

Answer 1

Para calcular a distância entre dois pontos, utilizamos a seguinte fórmula:

      $\Large\displaystyle\text{ \begin{gathered}\underline{\boxed{D_{ab}=\sqrt{(x_b-x_a)^2+(y_b-y_a)^2}}} \end{gathered} }$

Sabendo disso, temos que:

$\Large\displaystyle\begin{gathered}\mathbf{a)} \ D_{ab}=\sqrt{(5-(-1))^2+(2-2)^2}\end{gathered}$

$\Large\displaystyle\begin{gathered}D_{ab}=\sqrt{(6)^2+(0)^2}\end{gathered}$

$\Large\displaystyle\begin{gathered}D_{ab}=\sqrt{36}\end{gathered}$

$\Large\displaystyle\text{ \begin{gathered}\therefore \green{\underline{\boxed{D_{ab}=6}}}\ \ (\checkmark).\end{gathered} }$

$\Large\displaystyle\begin{gathered}\mathbf{b)} \ D_{ab}=\sqrt{(4-4)^2+(-3-1)^2}\end{gathered}$

$\Large\displaystyle\begin{gathered} \ D_{ab}=\sqrt{(0)^2+(-4)^2}\end{gathered}$

$\Large\displaystyle\begin{gathered} \ D_{ab}=\sqrt{16}\end{gathered}$

$\Large\displaystyle\text{ \begin{gathered}\therefore \green{\underline{\boxed{D_{ab}=4}}}\ \ (\checkmark).\end{gathered} }$

$\Large\displaystyle\begin{gathered}\mathbf{c)} \ D_{ab}=\sqrt{(5-2)^2+(1-3)^2}\end{gathered}$

$\Large\displaystyle\begin{gathered} D_{ab}=\sqrt{(3)^2+(-2)^2}\end{gathered}$

$\Large\displaystyle\text{ \begin{gathered} \therefore \green{\underline{\boxed{D_{ab}=\sqrt{13}}}}\ \ (\checkmark).\end{gathered} }$

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