Question

Calcule a distância entre os pontos A e B. a) A(2,4) e B(8,12)

Answer 1

Distância A(2,4) e B(8,12)
$D= \sqrt{(x-x0)^{2} +(y-y0)^{2} }$
$D= \sqrt{(8-2)^{2} +(12-4)^{2} }$
$D= \sqrt{(6)^{2} +(8)^{2} }$
$D= \sqrt{36 + 64 }$
$D= \sqrt{100 }$
D=10

Answer 2

$\large\boxed{\begin{array}{l} \sf{d_{AB }=\sqrt{(x_{A} -x_{B})^{2}+(y_{A} -y_{B})^{2}}} \\ \sf{d_{AB } = \sqrt{(2 - 8) {}^{2} + (4 - 12) {}^{2} } } \\ \sf{d_{AB } = \sqrt{( - 6) {}^{2} + ( - 8) {}^{2} } } \\ \sf{d_{AB } = \sqrt{36 + 64} } \\ \sf{d_{AB } = \sqrt{100} } \\ \huge\boxed{ \boxed{ \boxed{ \boxed{ \sf{d_{AB } = 10}}}}}\end{array}}$