find the equation of the median from b in ABC whose vertices are (1,5), B(5,3) and C(-3, -2)

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find the equation of the median from b in ABC whose vertices are (1,5), B(5,3) and C(-3, -2)

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Nguyệt Ánh 1 week 2021-07-22T04:32:07+00:00 1 Answers 2 views 0

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    2021-07-22T04:33:10+00:00

    Answer:

    y = x + 6

    x = 1

    y = ¼(x – 5) + 3

    Step-by-step explanation:

    Vetices are;

    A(1,5), B(5,3) and C(-3, -2)

    Thus;

    Median of AB is; D = (1 + 5)/2, (5 + 3)/2

    D = (3, 4)

    Median of BC is; E = (5 + (-3))/2, (3 + (-2))/2

    E = (1, 0.5)

    Median of AC is; F ; (-3 + 1)/2, (-2 + 5)/2

    F = (-1, 1.5)

    Thus, the median lines will be;

    CD, AE & BF.

    Thus;

    Equation of CD is;

    (y – (-3))/(x – (-2)) = (-2 – 4))/(-3 – 3)

    (y + 4)/(x + 2) = -6/-6

    y – 4 = 1(x + 2)

    y = 4 + x + 2

    y = x + 6

    Equation of AE;

    (y – 5)/(x – 1) = (0.5 – 5)/(1 – 1)

    (y – 5)/(x – 1) = -4.5/0

    Cross multiply to get;

    0(y – 5) = -4.5(x – 1)

    -4.5x = -4.5

    x = 1

    Equation of BF;

    (y – 3)/(x – 5) = (1.5 – 3)/(-1 – 5)

    (y – 3)/(x – 5) = -1.5/-6

    (y – 3)/(x – 5) = 1/4

    y – 3 = ¼(x – 5)

    y = ¼(x – 5) + 3

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