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Math Help - Line problems.

  1. #1
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    Post Line problems.

    Hey guys,

    I need help to solve the following problems:

    1) The line y - 2x + 3 = 0 intersects the curve y = x^2 - 2x at the point A and B. Find the co-ordinates of A and B.

    2) Determine whether the points A(-4, 3) B(-1, 5) and C(8, 11) are collinear.

    (In this question what does it mean by collinear?)

    Lastly..

    3) Find the point at which the line with the equation 3y - 12 = 4x cuts (i) the y-axis and (ii) the x-axis.

    Thanks looking forward for your reply.
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  2. #2
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    Quote Originally Posted by dadon
    Hey guys,

    I need help to solve the following problems:

    1) The line y - 2x + 3 = 0 intersects the curve y = x^2 - 2x at the point A and B. Find the co-ordinates of A and B.
    2) Determine whether the points A(-4, 3) B(-1, 5) and C(8, 11) are collinear.
    (In this question what does it mean by collinear?)
    Lastly..
    3) Find the point at which the line with the equation 3y - 12 = 4x cuts (i) the y-axis and (ii) the x-axis.
    Thanks looking forward for your reply.
    Hello,

    to 1): Transform the equation of the line to y = 2x-3. In the intersecting points the y-values of the line and the parabola must be equal:
    Solve 2x-3=x^2-2x.
    x^2-4x+3=0 ----> x = 3 or x = 1. Plug in these values into the equation of the line and you'll get: A(3,3) and B(1,-1).

    to 2)
    "collinear" means: forming a line. With 2 points, using the 2-point-formula of the line, you'll get an equation. Plug in the coordinates of the 3rd point and look if they fit into the equation:
    \frac{y-5}{x-(-1)}=\frac{3-5}{-4-(-1)} \Leftrightarrow y=\frac{2}{3} x+\frac{17}{3}
    Plug in the coordinates of C: 11=\frac{2}{3} 8+\frac{17}{3}
    11 = \frac{33}{3}\rightarrow C\in \mbox{line}

    to 3)
    (i): x = 0 ----> y = 4, so S(0 , 4)
    (ii): y = 0 ----> x = -3, so Z(-3 , 0)

    Greetings

    EB
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  3. #3
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    Thumbs up

    Thanks

    Could not have been explained any better!

    Kind Regards,

    dadon
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