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Math Help - Find Coordinates of Q

  1. #1
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    Find Coordinates of Q

    I come across problems like this all the time. How does one find the coordinates of a given variable on a line segment when one point and the midpoint are given? What is the easiest way to do this?

    Suppose that P is the endpoint of a segment PQ and M is the midpoint of PQ. Find the coordinates of Q.

    P(7, -4), M(8,5)
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by magentarita View Post
    I come across problems like this all the time. How does one find the coordinates of a given variable on a line segment when one point and the midpoint are given? What is the easiest way to do this?

    Suppose that P is the endpoint of a segment PQ and M is the midpoint of PQ. Find the coordinates of Q.

    P(7, -4), M(8,5)
    just use the midpoint formula. plug in what you know, and solve for what you don't know.

    Let Q = (x,y)

    then, \text{Midpoint (PQ)} = (8,5) = \left( \frac {x + 7}2, \frac {y - 4}2 \right)

    now equate the corresponding coordinates and solve for x and y
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  3. #3
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    Do you....

    Quote Originally Posted by Jhevon View Post
    just use the midpoint formula. plug in what you know, and solve for what you don't know.

    Let Q = (x,y)

    then, \text{Midpoint (PQ)} = (8,5) = \left( \frac {x + 7}2, \frac {y - 4}2 \right)

    now equate the corresponding coordinates and solve for x and y
    Do you mean like this?

    8 + 7/2 = y - 4/2

    15/2 = y - 4/2

    30 = 2y - 8

    30 - 8 = 2y

    22 = 2y

    22/2 = y

    11 = y

    Now do the same for x?

    Yes or no?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by magentarita View Post
    Do you mean like this?

    8 + 7/2 = y - 4/2

    15/2 = y - 4/2

    30 = 2y - 8

    30 - 8 = 2y

    22 = 2y

    22/2 = y

    11 = y

    Now do the same for x?

    Yes or no?
    no. i said equate corresponding components. that is, x-component with x-component and y-component with y-component

    thus you have:

    8 = (x + 7)/2

    and

    5 = (y - 4)/2

    now you can find x and y
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