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Perpendicular Lines
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What is to be learned? The rule connecting gradients and perpendicular lines.
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x y (2, 2) (7, 6) m = 6 – 2 7 – 2 = 4 / 5 (-2, 7) m = 7 – 2 -2 – 2 = - 5 / 4 m1m1 m2m2
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x y (1, 3) (8, 5) m = 5 – 3 8 – 1 = 2 / 7 (-1, 10) m = 10 – 3 -1 – 1 = - 7 / 2 m1m1 m2m2
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Summarising m1m2m1m2 4/54/5 2/72/7 -9 / 11 4 -5 / 4 -7 / 2 11 / 9 1 - ¼ 4 / 5 X - 5 / 4 = - 20 / 20 = -1 m 1 m 2 = -1
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For perpendicular lines m 1 m 2 = -1 If AB is ppdlr to CD Ex 1m AB = 6 / 7 Ex 2m AB = - 3 / 8 Ex 3m AB = 5 m AB = 0!!! m CD = - 7 / 6 m CD = 8 / 3 (5/1)(5/1) m CD = - 1 / 5 m CD = ∞
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Parallel and Perpendicular Which lines are perpendicular Which lines are parallel? y = 4x + 7y = ½x +2 y = ¼x y = – 5 + 4x y = -2x + 4y = 2x – 4
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