Distance from a point to a line

Text

Find the distance from $P(3,-2)$ to the line $r:\;4x-3y+1=0$.

Solution

Use the point-to-line distance formula: $d=\frac{|4\cdot 3-3\cdot(-2)+1|}{\sqrt{4^{2}+(-3)^{2}}}=\frac{|12+6+1|}{\sqrt{25}}=\frac{19}{5}=3.8.$ $\boxed{\,d=\tfrac{19}{5}=3.8\,}$