Distância do ponto à reta :
[tex]\displaystyle \text D = \frac{|\text a.\text x_o+\text b.\text y_o+\text c|}{\sqrt{\text a^2+\text b^2}}[/tex]
onde :
[tex]\text{a, b , c = coeficientes da reta } \\\\ \text x_o, \text y_o = \text {coordenadas do ponto}[/tex]
Temos a reta :
[tex]\text y = -\text x + 2 \ \therefore \ \text x+\text y -2= 0[/tex]
coeficientes : a = 1, b = 1, c = -2
Temos o ponto da origem : (0,0)
Aplicando distância do ponto até a reta ;
[tex]\displaystyle \text D =\frac{|1.0+1.0-2| }{\sqrt{1^2+1^2}} \\\\\\ \text D = \frac{|-2|}{\sqrt 2} \\\\\\ \text D =\frac{2}{\sqrt2}.\frac{\sqrt 2}{\sqrt2} \\\\\\ \text D = \frac{2\sqrt{2}}{2} \\\\\\ \huge\boxed{\text D = \sqrt{2}\ }\checkmark[/tex]
