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  1. #1
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    This is a question on a math university quiz.

    Find x and y such that the points A(-1,3), B(x,9) and C(5,y) are collinear with point B lying midway between points A and C.

    Well first, I did B-C=C-A as they are collinear, and now I'm stuck. Can anyone tell me how to do this question

    Thanks
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  2. #2
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    Quote Originally Posted by monkius View Post
    This is a question on a math university quiz.

    Find x and y such that the points A(-1,3), B(x,9) and C(5,y) are collinear with point B lying midway between points A and C.

    Well first, I did B-C=C-A as they are collinear, and now I'm stuck. Can anyone tell me how to do this question

    Thanks
    Hello monkius,

    If B is to be the midpoint, we must use the midpoint formula to determine the values of x and y.

    Midpoint=\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)

    Using points A and C, we substitute to get

    Midpoint=\left(\frac{5-1}{2}, \frac{y+3}{2}\right)

    Now, we know \frac{5-1}{2}=x

    Therefore, x = 2.

    We also know that \frac{y+3}{2}=9

    Therefore, y = 15.

    You can substitute these values back into points B and C to verify the slopes of AB, BC and AC are the same.

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