Question

In reperul cartezian se considera punctul A(1,2) si dreapta d: y=x-1. Calculați distanța de la punctul A la dreapta d

Answer 1

[tex](d): ax + by + c = 0 ,\ \ \ \ A(x_0,\ y_0). \\ \\ dist(A, d) = \dfrac{|ax_0+by_0+c|}{\sqrt{a^2+b^2}} [/tex]

[tex]\it (d): x-y-1=0,\ \ \ \ A(1,\ 2) \\ \\ dist(A,\ d)= \dfrac{|1-2-1|}{\sqrt{1+1}} = \dfrac{|-2|}{\sqrt2} = \dfrac{2}{\sqrt2} =\dfrac{\sqrt2\cdot\sqrt2}{\sqrt2} =\sqrt2[/tex]