Find the distance from the point $(5,1)$ to the line $y=2x+3$.

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Solve: Translating the coordinate axes so that $(5,1)$ becomes the center of the new coordinate system, the translation formula is $\left\{\begin{array}{l}x=x^{\prime}+5, \\ y=y^{\prime}+1\end{array}\right.$ The corresponding line equation will be $y^{\prime}+1=2\left(x^{\prime}+5\right)+3$. After rearrangement, it becomes $y^{\prime}=2 x^{\prime}+12$. Using the above method, it is easy to find $\mathrm{d}=\frac{|\mathrm{b}|}{\sqrt{1+\mathrm{m}^{2}}}$ $=\frac{12}{\sqrt{5}} \cdot$ (as shown in Figure 1)