Choose the one alternative that best completes the statement or answers the question.
-Let $P = ( x , y )$ be a point on the graph of $y = \sqrt { x }$. Express the distance $\mathrm { d }$ from $P$ to the point $( 1,0 )$ as a function of $x$
A) $d ( x ) = x ^ { 2 } = x + 1$
B) $d ( x ) = x ^ { 2 } + 2 x + 2$
C) $d ( x ) = \sqrt { x ^ { 2 } + 2 x + 2 }$
D) $d ( x ) = \sqrt { x ^ { 2 } - x + 1 }$

Question

Quizplus · Accepted Answer

The distance formula between two points $(x_1, y_1)$ and $(x_2, y_2)$ is $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$. For $P = (x, \sqrt{x})$ and $(1, 0)$, the distance is $\sqrt{(x - 1)^2 + (\sqrt{x} - 0)^2} = \sqrt{(x - 1)^2 + x} = \sqrt{x^2 - 2x + 1 + x} = \sqrt{x^2 - x + 1}$.

Choose the One Alternative That Best Completes the Statement or Answers