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​

Answer 1

$\sf \underline{Given} : -$

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)

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

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

$\sf 4y - 8 = 3x$

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