Question

what is an expression for the distance between the origin and a point p(x, y)?
a. d = 0
b. d = √(x² + y²)
c. d = √(x² - y²)
d. d = √(y² - x²)

Explanation:

Step1: Recall distance formula

The distance $d$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ in a two - dimensional plane is given by $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. When one point is the origin $(0,0)$ and the other point is $P(x,y)$, then $x_1 = 0,y_1 = 0,x_2=x,y_2 = y$.

Step2: Substitute values into formula

Substituting into the formula, we get $d=\sqrt{(x - 0)^2+(y - 0)^2}=\sqrt{x^{2}+y^{2}}$.

Answer:

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