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Math Help - Endpoint question

  1. #1
    Senior Member euclid2's Avatar
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    Endpoint question

    GivenP(-7,2) is one endpoint of the line segment PQ and M(-5,6) is the midpoint of PQ, find the coordinates of the other endpoint Q.

    Thanks alot in advance
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  2. #2
    Senior Member nikhil's Avatar
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    If a and b are ordinate or abcissa of two points then mid point say c is given by
    c=(a+b)/2
    in your question,mid point is given.
    So let us consider the abcissa first
    -5=(-7+a)/2
    a-7=-10
    a=-3
    hence the abcissa of the end point is -3.similarly you can find the ordinate of the end point.
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  3. #3
    Senior Member euclid2's Avatar
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    Is the other coordinate 6?
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  4. #4
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    Quote Originally Posted by euclid2 View Post
    GivenP(-7,2) is one endpoint of the line segment PQ and M(-5,6) is the midpoint of PQ, find the coordinates of the other endpoint Q.

    Thanks alot in advance
    Quote Originally Posted by euclid2 View Post
    Is the other coordinate 6?
    No... Call the point Q = (a,b) and lets follow Nikhil's idea:

    \frac{(-7,2) + (a,b)}{2} = (-5,6)

    But now let us solve it together,

    (-7,2) + (a,b) = 2(-5,6) = (-10,12)

    (-7,2) + (a,b) = (-7+a,2+b) = (-10,12)

    (-7+a,2+b) = (-10,12) \Rightarrow -7+a = -10, 2+b = 12 \Rightarrow a=-3,b=10

    Thus Q(-3,10) is the other end point.
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  5. #5
    Senior Member euclid2's Avatar
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    Ok thanks, thats where I got confused and divided instead of subtracted.
    (-7+x)/2=-5
    -7x=-10
    x=-3
    (2x+y)/2=6
    2y=6*2
    y=12-2-where i divided instead, my mistake
    y=10

    Thanks.
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