Matematika

Pertanyaan

Bantu yaaa,, pakai caraa
Bantu yaaa,, pakai caraa

1 Jawaban

  • a. garis g yang melalui titik (3,-6) dan sejajar 3y - 4x + 6 = 0
    =======================
    3y - 4x + 6 = 0
    3y = 4x - 6
      y = (4/3)x - 2  >> m=(4/3)
    =======================
    Pers. garis g adalah
    y + 6 = (4/3)(x - 3)
    y = (4/3)x - 4 - 6
    y = (4/3)x - 10
    3y - 4x + 10 = 0


    b. garis h yang melalui titik (3,-2) dan tegak lurus 3y - 2x + 3 = 0
    =======================
    3y - 2x + 3 = 0
    3y = 2x - 3
      y = (2/3)x - 1  >> m=(2/3)
    =======================
    garis h tegak lurus dengan garis y = (2/3)x - 1, maka gradien garis h adalah
    -(3/2)
    Sehingga pers. garis h
    y + 2 = -(3/2)(x - 3)
    y = -(3/2)x + 9/2 - 2
    y = -(3/2)x + 5/2
    y = (-3x + 5) / 2
    2y = -3x + 5
    2y + 3x - 5 = 0


    c. garis L melalui titik (-2,4) dan tegak lurus garis k yang melalui titik (-5,6) dan (9,1)
    ====================
    gradien garis k
    m = (y2-y1) / (x2-x1)
    m = (6 -1) / (-5 - 9)
    m = -(5/14)
    =====================
    karena garis L tegak lurus garis k, maka gradien garis k adalh
    m = (14/5)
    Pers. garis k
    y - 4 = (14/5)(x + 2)
    y = (14/5)x + 28/5 + 4
    y = (14/5)x + 48/5
    y = (14x + 48) / 5
    5y - 14x - 48 =0