To show that two perpendicular lines, neither of which is
Chapter 1, Problem 43E(choose chapter or problem)
To show that two perpendicular lines, neither of which is vertical, have slopes with a product of –1, go through the following steps. Let line L1 have equation y = m1x + b1, and let L2 have equation y = m2x + b2, with m1 >0 and m2 < 0. Assume that L1 and L2 are perpendicular, and use right triangle MPN shown in the figure. Prove each of the following statements.a.MQ has length m1.b.QN has length ?m2.c. Triangles MPQ and PNQ are similar.d.m1 /1 = 1/(?m2) and m1m2 = ?1
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