To show that two perpendicular lines, neither of which is vertical, have slopes with a product of
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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 = m1 x + 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 m1 m2 = -1
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a See the figure in the textbook Segment MN is drawn perpendicular to segme...View the full answer
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