Ecuația dreptei AC este:
[tex]\it \dfrac{y-y_A}{y_C-y_A} =\dfrac{x-x_A}{x_C-x_A} \Rightarrow \dfrac{y-9}{-3-9}= \dfrac{x-0}{5-0} \Rightarrow \dfrac{y-9}{-12}= \dfrac{x}{5} \Rightarrow y-9= \dfrac{-12x}{5}\Rightarrow\\ \\ \\ \Rightarrow y=-\dfrac{12}{5}x+9 \Rightarrow panta\ lui\ AC\ este\ m=- \dfrac{12}{5}[/tex]
Ecuația unei perpendiculare pe AC este:
[tex]\it y= m'x+n,\ unde\ m'=- \dfrac{1}{m}=-\dfrac{1}{-\dfrac{12}{5}}=\dfrac{5}{12}\\ \\ \\ Acum,\ ecua\c{\it t}ia\ perpendicularei\ devine:\\ \\ y=\dfrac{12}{5}x+n\ \ \ \ (1)[/tex]
Dacă perpendiculara pe AC trece prin B(2, -1), vom avea în (1) :
[tex]\it -1=\dfrac{5}{12}\cdot2+n \Rightarrow -1=\dfrac{5}{6}+n \Rightarrow n=-1-\dfrac{5}{6} \Rightarrow n=-\dfrac{11}{6}\ \ \ \ \ (2)\\ \\ \\ (1),\ (2) \Rightarrow y=\dfrac{5}{12}x-\dfrac{11}{6}\ \ (ecua\c{\it t}ia\ \^in\breve{a}l\c{\it t}imii\ duse\ din\ B)[/tex]
