Determine the point that partitions line segment ((1,1),(6,6)) into a 3:7 ratio. Show work please

Question

Determine the point that partitions line segment ((1,1),(6,6)) into a 3:7 ratio. Show work please

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Bella 5 days 2021-11-25T13:28:38+00:00 1 Answer 0 views 0

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    2021-11-25T13:30:18+00:00

    Answer:

    P\left(\frac{5}{2},\frac{5}{2}\right)  is the point that partitions line segment ((1,1),(6,6)) into a 3:7 ratio.

    Step-by-step explanation:

    Let AB is the line segment with A having the coordinates (1, 1) and B having the coordinates (6, 6)

    Let us consider the point P(x, y) partitions the line segment AB into a ratio 3:7

    Considering the formula to find the coordinates of P(x, y)

    • x=\frac{m_1x_2+m_2x_1}{m_1+m_2}
    • y=\frac{m_1y_2+m_2y_1}{m_1+m_2}

    From the data,

    m_1=3,\:\:m_2=7,\:\:x_1=1,\:\:x_2=6,\:\:y_1=1,\:\:y_2=6

    so

    x=\frac{m_1x_2+m_2x_1}{m_1+m_2}

    x=\frac{\left(3\right)\left(6\right)+\left(7\right)\left(1\right)}{\left(3+7\right)}

    x=\frac{25}{3+7}

    x=\frac{25}{10}

    x=\frac{5}{2}

    also

    y=\frac{m_1y_2+m_2y_1}{m_1+m_2}

    y=\frac{\left(3\right)\left(6\right)+\left(7\right)\left(1\right)}{\left(3+7\right)}

    \:y=\frac{25}{3+7}

    y=\frac{25}{10}

    y=\frac{5}{2}

    Therefore, P\left(\frac{5}{2},\frac{5}{2}\right)  is the point that partitions line segment ((1,1),(6,6)) into a 3:7 ratio.

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