Question

Calcule a distância entre os pontos dados:
A) A ( 1,1) B (3,1)
B) A (-2,2) B (1,-3)​

Answer 1

A)

$d = \sqrt{ {(3 - 1)}^{2} + {(1 - 1)}^{2} } = 2$

B)

$d = \sqrt{ {(1 - ( - 2))}^{2} + {( - 3 - 2)}^{2} } = \sqrt{34}$

Answer 2

A)

$\large \boxed{ \begin{array}{l} \sf{\sf{d_{A,B} = \sqrt{(x_A - x_B) {}^{2} + (y_A - y_B) {}^{2} } }} \\ \\ \sf{d_{A,B} = \sqrt{(1 - 3) {}^{2} + (1 - 1) {}^{2} } } \\ \\ \sf{d_{A,B} = \sqrt{( - 2) {}^{2} + 0 {}^{2} } } \\ \\ \sf{d_{A,B} = \sqrt{4 + 0} } \\ \\ \sf{d_{A,B} = \sqrt{4} } \\ \\ \boxed{\sf{d_{A,B} = 2} } \blue{ \checkmark}\end{array}}$

B)

$\large \boxed{ \begin{array}{l} \sf{\sf{\sf{d_{A,B} = \sqrt{(x_A - x_B) {}^{2} + (y_A - y_B) {}^{2} } }}} \\ \\ \sf{d_{A,B} = \sqrt{( ( - 2) - 1) {}^{2} + (2 - ( - 3)) {}^{2} } } \\ \\ \sf{d_{A,B} = \sqrt{( - 3) {}^{2} + 5 {}^{2} } } \\ \\ \sf{d_{A,B} = \sqrt{9 + 25} } \\ \\ \boxed{\sf{d_{A,B} = \sqrt{34}}} \blue{ \checkmark}\end{array}}$