To find the distance between the origin (0, 0) and a point [tex]\( P(x, y) \)[/tex], we use the distance formula. The distance formula for two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by:
[tex]\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]
In our case, the origin has coordinates [tex]\((0, 0)\)[/tex] and the point [tex]\( P \)[/tex] has coordinates [tex]\((x, y)\)[/tex]. Plugging these coordinates into the distance formula, we obtain:
[tex]\[ d = \sqrt{(x - 0)^2 + (y - 0)^2} \][/tex]
Simplifying this expression, we get:
[tex]\[ d = \sqrt{x^2 + y^2} \][/tex]
Thus, the correct expression for the distance between the origin and the point [tex]\( P(x, y) \)[/tex] is:
[tex]\[ \boxed{d = \sqrt{x^2 + y^2}} \][/tex]
Among the given options, the correct choice is:
B. [tex]\( d = \sqrt{x^2 + y^2} \)[/tex]
