Question

A(0,3) B(4,8) C(4,0) distanta de la B la AC in reperul cartezian xOy

Answer 1

$\displaystyle AC:\frac{x-x_C}{x_A-x_C}=\frac{y-y_C}{y_A-y_C}\Rightarrow \frac{x-4}{0-4}=\frac{y-0}{3-0}\\\\\Rightarrow AC: 3x+4y-12=0\\d(B, AC)=\frac{|a\cdot x_B+b\cdot y_B+c|}{\sqrt{a^2+b^2}}=\frac{|3\cdot4+4\cdot8-12|}{\sqrt{3^2+4^2}}=\frac{32}{5}$