Question

1- Determine a
distância entre

os pontos

P(-1,10) e

Q(5,2).


2- Calcule a
distância entre os

pontos A(1,3) e

B(7,2).​

Answer 1

Resposta:

1)

Solução:

$\large \sf \displaystyle \left\begin{array}{l l l l l } \sf d_{PQ} = \sqrt{(x_Q - x_P)^2+(y_Q - y_P)^2} \end{array}\right$

$\large \sf \displaystyle \left\begin{array}{l l l l l } \sf d_{PQ} = \sqrt{(5 - (-1))^2+(2 - 10)^2} \end{array}\right$

$\large \sf \displaystyle \left\begin{array}{l l l l l } \sf d_{PQ} = \sqrt{(5 +1)^2+( - 8)^2} \end{array}\right$

$\large \sf \displaystyle \left\begin{array}{l l l l l } \sf d_{PQ} = \sqrt{(6)^2+ 64} \end{array}\right$

$\large \sf \displaystyle \left\begin{array}{l l l l l } \sf d_{PQ} = \sqrt{36+ 64} \end{array}\right$

$\large \sf \displaystyle \left\begin{array}{l l l l l } \sf d_{PQ} = \sqrt{100} \end{array}\right$

$\framebox{ \boldsymbol{ \sf \displaystyle \large \sf \displaystyle \left\begin{array}{l l l l l } \sf d_{PQ} = 10 \end{array}\right }} \quad \gets \mathbf{ Resposta }$

2)

$\large \sf \displaystyle \left\begin{array}{l l l l l } \sf d_{AB} = \sqrt{(x_B - x_A)^2+(y_B - y_A)^2} \end{array}\right$

$\large \sf \displaystyle \left\begin{array}{l l l l l } \sf d_{AB} = \sqrt{(7- 1)^2+(2 - 3)^2} \end{array}\right$

$\large \sf \displaystyle \left\begin{array}{l l l l l } \sf d_{AB} = \sqrt{(6)^2+(- 1)^2} \end{array}\right$

$\large \sf \displaystyle \left\begin{array}{l l l l l } \sf d_{AB} = \sqrt{36+1} \end{array}\right$

$\framebox{ \boldsymbol{ \sf \displaystyle \large \sf \displaystyle \left\begin{array}{l l l l l } \sf d_{PQ} = \sqrt{37} \end{array}\right }} \quad \gets \mathbf{ Resposta }$

Explicação passo-a-passo: