Question

what is an expression for the distance between the origin and a point p(x, y)?
a. d = 0
b. d = \sqrt{x^{2}+y^{2}}
c. d = \sqrt{x^{2}-y^{2}}
d. d = \sqrt{y^{2}-x^{2}}

Explanation:

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step2: Identify points

The origin is $(0,0)$ and the point is $P(x,y)$. So $x_1 = 0,y_1 = 0,x_2=x,y_2 = y$.

Step3: Substitute values

Substitute into the formula: $d=\sqrt{(x - 0)^2+(y - 0)^2}=\sqrt{x^{2}+y^{2}}$.

Answer:

B. $d = \sqrt{x^{2}+y^{2}}$