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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1. [tex] \sf \underline{Given} : -[/tex]

   P = (2,1)

   Q = (-2,3)

   R = (4,5)

   [tex] \sf \underline{To \: find} : – [/tex]

   The equation of the median through the vertex R

   [tex] \sf \underline{Solution} : – [/tex]

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

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

   Let M be the mid point of PQ

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

   [tex] \sf M= \bigg( \dfrac{2 – 2}{2},\dfrac{1 + 3}{2} \bigg)[/tex]

   [tex] \sf M= \bigg( \dfrac{0}{2},\dfrac{4}{2} \bigg)[/tex]

   [tex] \sf M= (0,2)[/tex]

   The slope of medium PM,

   [tex] \sf m = \dfrac{5 – 2}{4 – 0} = \dfrac{3}{4} [/tex]

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

   [tex] \sf y – y_1 = m(x – x_1)[/tex]

   [tex] \sf y -2 = \dfrac{3}{4} (x – 0)[/tex]

   [tex] \sf 4y – 8 = 3x[/tex]

   [tex]\boxed{ \sf3x – 4y + 8 = 0}[/tex]

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