? asked in 科學及數學數學 · 1 decade ago

Rectangle Coordinates System

The line joining the points A(-3,5) and B(11,-5) cuts the line L : y = x at the point P and the x-axis at the point Q.

a) Find the coordinates of P and Q.

b) Hence, or otherwise, find the ratios AP : PQ : QB

1 Answer

Rating
  • choy
    Lv 5
    1 decade ago
    Favorite Answer

    a)

    Eqn. of line AB:

    (5 - -5)/(-3 - 11) = (y-5)/(x - -3)

    -10/14 = (y-5)/(x + 3)

    14(y-5)= -10(x + 3)

    14y - 70 = -10x - 30

    10x + 14y - 40 = 0

    5x + 7y - 20 = 0 -------(1)

    Put x=y into (1),

    5y + 7y - 20 = 0

    12y = 20

    y = 5/3

    x = y = 5/3

    P is (5/3 , 5/3)

    Put y=0 into (1),

    5x + 7 x 0 - 20 = 0

    5x = 20

    x = 4

    Q is (4 , 0)

    b)

    AP : PQ : QB

    = (5/3 - -3) : (4 - 5/3) : (11 - 4)

    = (5/3 + 3) : (4 - 5/3) : (11 - 4)

    = 14/3 : 7/3 : 7

    = 14 : 7 : 21

Still have questions? Get your answers by asking now.