Answer:
Problem 1) [tex] m = \dfrac{1}{4} [/tex] [tex] slope_{perpendicular} = -4 [/tex]
Problem 2) [tex] m = \dfrac{1}{3} [/tex] [tex] slope_{perpendicular} = -3 [/tex]
Step-by-step explanation:
[tex] slope = m = \dfrac{y_2 - y_1}{x_2 - x_1} [/tex]
[tex] slope_{perpendicular} = \dfrac{-1}{m} [/tex]
Problem 1) M(9,6), N(1,4)
[tex] slope = m = \dfrac{6 - 4}{9 - 1} = \dfrac{2}{8} = \dfrac{1}{4} [/tex]
[tex] slope_{perpendicular} = \dfrac{-1}{\frac{1}{4}} = -4 [/tex]
Problem 2) M(-2,2), N(4,-4)
[tex] slope = m = \dfrac{4 - 2}{4 - (-2)} = \dfrac{2}{6} = \dfrac{1}{3} [/tex]
[tex] slope_{perpendicular} = \dfrac{-1}{\frac{1}{3}} = -3 [/tex]
