NCERT Solutions
Class 11 Maths
Straight Lines

Ex.10.2 Q.9
The vertices of ∆PQR are P (2, 1), Q (–2, 3) and R (4, 5). Find equation of the median through the vertex R.
It is given that the vertices of ∆PQR 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 {(2 - 2) ÷ 2, (1 + 3) ÷ 2} = (0, 2)
It is known that the equation of the line passing through points (x1, y1) and (x2, y2) is
(y – y1) = {(y2 – y1) ÷ (x2 – x1)} (x – x1)
Therefore, the equation of RL can be determined by substituting
(x1, y1) = (4, 5) and (x2, y2) = (0, 2)
(y – 5) = {(2 – 5) ÷ (0 - 4)} (x - 4)
=> (y – 5) = (-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