Answer
The distance from a point $P\left( x,y \right)$ to $\left( 2,0 \right)$ in terms of the point’s $x\text{-coordinate}$ is, $d=\sqrt{{{x}^{2}}-3x+4}$.
Work Step by Step
The distance from point $P\left( x,y \right)$ to point $\left( 2,0 \right)$ is
$\begin{align}
& d=\sqrt{{{\left( x-2 \right)}^{2}}+{{\left( y-0 \right)}^{2}}} \\
& =\sqrt{{{\left( x-2 \right)}^{2}}+{{y}^{2}}}
\end{align}$
Substitute $\sqrt{x}$ for $y$ in the above equation,
$d=\sqrt{{{\left( x-2 \right)}^{2}}+{{\left( \sqrt{x} \right)}^{2}}}$
Use the formula ${{\left( A-B \right)}^{2}}={{A}^{2}}-2AB+{{B}^{2}}$ in the above equation,
$\begin{align}
& d=\sqrt{{{x}^{2}}-4x+4+x} \\
& =\sqrt{{{x}^{2}}-3x+4}
\end{align}$
The required distance from a point $P\left( x,y \right)$ from point $\left( 2,0 \right)$ in terms of the point’s $x\text{-coordinate}$ is, $d=\sqrt{{{x}^{2}}-3x+4}$.
