To determine the distance $d$ from the point $P\left(x_{1}, y_{1}\right)$ to the line $A x+B y+C=0,$ proceed as follows: Consider Figure 15 .

Assume neither $A$ nor $B$ is zero. (If either was zero, the problem is trivial, why?) Draw the vertical line from $P$ to $T$. (a) Show that $\angle P S R=\angle T S W$, (b) Show that

$\angle R P S=\angle S W T .$ (c) Show that $\Delta P R S$ is similar to triangle $\Delta W O Q$. (d) Find the coordinates of $Q, W$ and $S$. (e) By similarity, conclude that $$\frac{d}{O W}=\frac{P R}{Q W}$$ (e) Substitute for these distances and simplify, to show that $d=\frac{\left|A x_{1}+B y+C\right|}{\sqrt{A^{2}+B^{2}}}$ (Note, the absolute value was included as distance must always be positive.)