Question

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

Answer 1

It is given that the vertices of ΔPQR are P (2, 1), Q (2, 3), and R (4, 5).
Let RL be the median through vertex R.
Accordingly, L is the mid-point of PQ.
By mid-point formula, the coordinates of point L are given by $(\frac {2-2}{2},\frac {1+3}{2})=(0,2)$
$y-y_1 = \frac {y_2-y_1}{x_2-x_1}(x-x_1)$

It is known that the equation of the line passing through points (x1, y1) and (x2, y2) is.
So, the equation of RL can be determined by substituting (x1, y1) = (4, 5) and (x2, y2) = (0, 2).
Hence,
$y-5=\frac {2-5}{0-4}(x-4)$
⇒ $y-5=\frac {-3}{-4}(x-4)$
⇒ $4(y-5)=3(x-4)$
⇒ $4y-20=3x-12$
⇒ $3x-4y+8=0$

Thus, the required equation of the median through vertex R is $3x-4y+8 = 0$.