Question

Find the equation of the line passing through the point ( -4, -5) and perpendicular to the line joining the points (1, 2) and (5, 6)?

Answer 1

$$\begin{gathered} \mathrm{Slop}\mathrm{of}\mathrm{line}\mathrm{passing}\mathrm{through}\left(1,2\right)\mathrm{and}\left(5,6\right) \\ =\frac{6-2}{5-1}=1 \\ \mathrm{So}\mathrm{slop}\mathrm{of}\mathrm{line}\mathrm{perpendicular}\mathrm{to}\mathrm{it}=\frac{1}{-1}=-1 \\ \mathrm{Now}\mathrm{equation}\mathrm{of}\mathrm{line}\mathrm{passing}\mathrm{through}\left(-4,-5\right)\mathrm{and}\mathrm{having}\mathrm{slop}-1\mathrm{is}, \\ \mathrm{y}+5=-1\left(\mathrm{x}+4\right) \\ \mathrm{x}+\mathrm{y}+9=0 \end{gathered}$$