Step 1:
Line A and line B are parallel if the slope of line A is equal to the slope of line B
Line A and line B are perpendicular if the product of the slope of line A and the slope of line B is equal to - 1.
Step 2:
Line A has points (-1,3) and (5,1)
Line B has points (-2,3) and (0,9)
Next, find the slope of lines A and B
[tex]\begin{gathered} \text{For line A} \\ x_1\text{ = -1} \\ y_1\text{ = 3} \\ x_2\text{ = 5} \\ y_2\text{ = 1} \\ \text{Slope = }\frac{y_2-y_1}{x_2-x_1}\text{ } \\ =\text{ }\frac{1\text{ - 3}}{5\text{ + 1}} \\ =\text{ }\frac{-2}{6} \\ =\text{ }\frac{-1}{3} \\ \text{Slope of line A = }\frac{-1}{3} \end{gathered}[/tex][tex]\begin{gathered} \text{For line B} \\ x_1=-2,y_1\text{ = 3} \\ x_2=0,y_2\text{ = 9} \\ \text{Slope = }\frac{9\text{ - 3}}{0\text{ + 2}} \\ =\text{ }\frac{6}{2} \\ \text{Slope of line B = 3} \end{gathered}[/tex]
Step 3:
Line A is not parallel to line B since the slope of A is not equal to the slope of B.
[tex]\begin{gathered} \text{Hence} \\ L\text{ine A is perpendicular to line B because } \\ \text{Slope of line A }\times\text{ Slope of line B = -1} \\ \frac{-1}{3}\text{ }\times\text{ 3 = -1} \end{gathered}[/tex]
Final answer
The lines are perpendicular.
