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Math Help - Is the point on the line?

  1. #1
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    Is the point on the line?

    Determine if each point P is on the line [x,y] = [2,-3] + t[4,7]
    a) P(-2,-10)
    b) P(6,5)
    c) p(10,14)
    d) P(4, 0.5)

    Answers: Yes, No, No, Yes

    We just learned this today and I'm not sure of the difference between vector r and vector "r not" from r = r0 + tm. I'm not sure where to substitute the given points.
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  2. #2
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    Quote Originally Posted by TN17 View Post
    Determine if each point P is on the line [x,y] = [2,-3] + t[4,7]
    a) P(-2,-10)
    b) P(6,5)
    c) p(10,14)
    d) P(4, 0.5)
    Answers: Yes, No, No, Yes
    To be absolutely clear, you need to give a value for t in every yes answer.
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  3. #3
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    Quote Originally Posted by TN17 View Post
    Determine if each point P is on the line [x,y] = [2,-3] + t[4,7]
    a) P(-2,-10)
    b) P(6,5)
    c) p(10,14)
    d) P(4, 0.5)

    Answers: Yes, No, No, Yes

    We just learned this today and I'm not sure of the difference between vector r and vector "r not" from r = r0 + tm. I'm not sure where to substitute the given points.
    x = 2+4t solve for t in terms of x ...

    t = \dfrac{x-2}{4}


    y = -3+7t

    substitute for t ...

    y = -3 + 7 \cdot \dfrac{x-2}{4}

    now check the points ...
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