Question

Show that two lines with slopes m1 and m2 are

(i) parallel iff m1 = m2

(ii) perpendicular iff m1 m2 = -1.

Answer 1

(i) Let the lines l1 and l2 have slopes m1and m2 respectively and their respective inclinations be α and β.

∴ tan α = m1 and tan β = m2 If l1 is parallel to l2 then α = β

∴ tan α = tan β Conversely, if m1= m2, then tan α = tanβ ⇒ α = β lines are parallel

(ii) If l1 and l2 are perpendicular then P = 90° + α