? asked in 科學及數學數學 · 1 decade ago

Rectangle Coordinates System

Given the points A(-1,3) and B(5,-8).

P is a point on the line segment AB such that AP : PB = r : 1.

a) Find the coordinates of P in terms of r.

b) Hence, find the ratio in which the line x - 2y - 5 = 0 divides the line segment AB

1 Answer

Rating
  • choy
    Lv 5
    1 decade ago
    Favorite Answer

    a)

    let P be (x,y)

    x = (1(-1) + r(5))/(1 + r) = (5r - 1)/(1 + r)

    y = (1(3) + r(-8))/(1 + r) = (3 - 8r)/(1 + r)

    ans: P is ((5r - 1)/(1 + r) , (3 - 8r)/(1 + r))

    b)

    assume line AB and the line x - 2y - 5 = 0 intercept at P

    Put P into the eqn., we have

    (5r - 1)/(1 + r) - 2(3 - 8r)/(1 + r) - 5 = 0

    (5r - 1) - 2(3 - 8r) - 5(1 + r) = 0

    5r - 1 - 6 + 16r - 5 - 5r = 0

    16r = 12

    r = 12/16 = 3/4

    AP : PB = r : 1 = 3/4 : 1 = 3 : 4

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