Find the length of the perpendicular drawn from the point (–2,–3) to the straight line 5x – 2y + 4 = 0.

The length of the perpendicular drawn from the point $\mathrm{P}\left({\mathrm{x}}_1,{\mathrm{y}}_1\right)\text{ to the st.line }$
$\mathrm{ax}+\mathrm{by}+\mathrm{c}=0\text{ is }\mathrm{d}=\frac{\left|{\mathrm{ax}}_1+{\mathrm{by}}_1+\mathrm{c}\right|}{\sqrt{{\mathrm{a}}^2+{\mathrm{b}}^2}}$
given st.line $5\mathrm{x}-2\mathrm{y}+4=0$
and given point (–2, –3)
$\therefore \text{ the perpendicular distance from }(-2,-3)\text{ to }$the st.line
$\mathrm{d}=\frac{\left|5\right(-2)-2(-3)+4|}{\sqrt{25+4}}=\frac{|-10+6+4|}{\sqrt{29}}=0$