Question

Calcule a distância entre os pontos dados abaixo:

a) A (2,5) e B (-5, -2)
b) C (2,3) e D(-2, -2)​

Answer 1

$\boxed{\begin{array}{l}\tt a)~\sf\Delta\!~x=-5-2=-7\\\sf\Delta\!~y=-2-5=-7\\\sf d_{A,B}=\sqrt{\Delta\!~x^2+\Delta\!,y^2}\\\sf d_{A,B}=\sqrt{(-7)^2+(-7)^2}\\\sf d_{A, B} =\sqrt{49+49}\\\sf d_{A, B} =\sqrt{2\cdot49}\\\sf d_{A, B}=7\sqrt{2}\\\tt b)~\sf \Delta\!~x=-2-2=-4\\\sf\Delta\!~y=-2-3=-5\\\sf d_{C,D}=\sqrt{(-4)^2+(-5)^2}\\\sf d_{C, D} =\sqrt{16+25}\\\sf d_{C, D}=\sqrt{41}\end{array}}\blue{\checkmark}$