[tex]We\text{ have to find the slope of the lines, if the product of the slopes is -1, then they are perpendicular!}[/tex][tex]\begin{gathered} m_{AC}=\frac{7-1}{5-(-2)} \\ m_{AC}=\frac{6}{7} \\ \\ \\ m_{BC}=\frac{4-(-3)}{-3-3} \\ m_{BC}=\frac{7}{-6}=-\frac{7}{6} \end{gathered}[/tex][tex]\begin{gathered} m_{AC}\cdot m_{BD}=\frac{6}{7}\times(-\frac{7}{6}) \\ =-1 \\ \\ \text{ Thus the lines are perpendicular} \end{gathered}[/tex]
