The vertices of ΔPQR are P (2, 1), Q (–2, 3) and R (4, 5). Find equation of the median through the vertex R.

Vertices of ΔPQR i.e. P (2, 1), Q (-2, 3) and R (4, 5)

Let RL be the median of vertex R.

So, L is a midpoint of PQ.

We know that the midpoint formula is given by

\( (\dfrac{x_1+x_2}{2}, \dfrac{y_1+y_2}{2})\)

\( (\dfrac{2-2}{2}, \dfrac{1+3}{2})\)  = (0, 2)

We know that the equation of the line passing through the points (x₁, y₁) and (x₂, y₂) is given by
\( y-5= \dfrac{2-5}{0-4}(x-4)\)

\( y-5= \dfrac{-3}{-4}(x-4)\)

(-4) (y – 5) = (-3) (x – 4)

-4y + 20 = -3x + 12

-4y + 20 + 3x – 12 = 0

3x – 4y + 8 = 0

The equation of median through the vertex R is 3x – 4y + 8 = 0.