Geometry

The midpoint of uv is (5 -11). the coordinates of one endpoint are u(3 5) find the coordinates of endpoint v. I really need help asap! i have to put this in today..

Please and thank you!

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  1. let the other endpoint be (x,y)

    I will find the x, then you find the y using the same method.

    for the x:
    (x+3)/2 = 5
    x+3 = 10
    x = 7

    for the y:
    ......

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  2. I don't know... i don't get it..

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  3. the midpoint is just the average of the two endpoints.

    Play around with a few numbers, and you will see that this is true.

    Think of it this way.

    You start at a, and b is halfway to c.

    That is, (b-a) = (c-b)

    The midpoint b can then be found:

    b-a = c-b
    2b = a+c
    b = (a+c)/2

    That's Reiny's method. Use that equation to find c.

    Or, if you want to find c, then you can use

    b-a = c-b
    c = 2b-a
    c = 2*5 - 3 = 7

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  4. haha i know lol

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  5. The answer is (7,-27)

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  6. yes but how?

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  7. (5,-11)=(3+x/2),(5+y/2)
    5=3+x/2
    Multiply each side by 2 and simplify.
    -11=5+x/2
    Multiply each side by 2 and simplify.

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  8. logan paul

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  9. there are two ways to solve.
    the x value on point u is two away from the x value on the midpoint. two away from 5 is 7 so point v's x value is 7. the y value on u is 6 away from the y value on the midpoint. 6 away from 11 is 17 so v's y value is 17. v = (7 , 17)
    the midpoint = (x1 + x2 / 2) + (y1 + y2 / 2)
    (3 + x / 2) = 5
    2 * (3 + x / 2) = 5 * 2 (this cancels put the /2 in the beginning of the problem)
    (3 + x) = 10
    -3 -3
    x = 7
    (5 + y / 2) = 11
    multiply both sides by 2 again
    (5 + y) = 22
    subtract both sides by 5
    y = 17

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