Matematika

Pertanyaan

persamaan garis yang melalui titik (-3,-3) dan tegak lurus garis y=-6x+2 adalah...a).6x-y=15. b).6x-y=-15. c).x-6y=15. d).x-6y=-15

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2 Jawaban

  • m1 = (-6) m2 = -1/m1
    = -1/-6
    = 1/6
    y-y1=m(x-x1)
    y-(-3)=1/6(x-(-3))
    y+3 = 1/6(x+3)
    6y+18 = x+3
    x-6y = -15 (D)
  • Dua garis tegak lurus memenuhi syarat m₁ . m₂ = -1

    y = -6x + 2 ....memiliki gradien (m₂) = -6

    m₁ . m₂ = -1
    m₁ . (-6) = -1
    m₁ = 1/6

    Persamaan garis melewati (-3,-3)
    y - y₁ = m₁ (x - x₁)
    y - (-3) = (1/6) (x - (-3))
    y + 3 = (1/6) x + (3/6)
    y = (1/6) x + (3/6) - 3
    y = (1/6) x + (3/6) - (18/6)
    y = (1/6) x - (15/6) ..................... dikalikan (6)
    6y = x - 15
    6y - x = -15 ......................dikalikan (-1)
    x - 6y = 15 ...................................................Jawaban (d)

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