the vertices of triangle PQR are P(2,1), Q(-2,3) and R(4,5) Find the equation of the median through the vertex R​

Question

the vertices of triangle PQR are P(2,1), Q(-2,3) and R(4,5) Find the equation of the median through the vertex R​

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Sarah 3 months 2021-07-17T12:42:23+00:00 1 Answers 0 views 0

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    2021-07-17T12:43:37+00:00

     \sf  \underline{Given} :  -

    P = (2,1)

    Q = (-2,3)

    R = (4,5)

     \sf  \underline{To \:  find} : -

    The equation of the median through the vertex R

     \sf  \underline{Solution} : -

    The coordinates of the mid point M of the joining AP(x₁, y₁) and Q (x₂, y₂) is

     \sf  M= \bigg( \dfrac{x_1 + x_2}{2},\dfrac{y_1 + y_2}{2} \bigg)

    Let M be the mid point of PQ

     \sf  M= \bigg( \dfrac{x_1 + x_2}{2},\dfrac{y_1 + y_2}{2} \bigg)

     \sf  M= \bigg( \dfrac{2 - 2}{2},\dfrac{1 + 3}{2} \bigg)

     \sf  M= \bigg( \dfrac{0}{2},\dfrac{4}{2} \bigg)

     \sf  M= (0,2)

    The slope of medium PM,

     \sf m =  \dfrac{5 - 2}{4 - 0}  =  \dfrac{3}{4}

    The Equation of the medium PM is y – y₁ = m(x – x₁)

     \sf y - y_1 = m(x - x_1)

     \sf y -2 =  \dfrac{3}{4} (x - 0)

     \sf 4y - 8 = 3x

    \boxed{ \sf3x - 4y + 8 = 0}

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