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

Solution:

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 midpoint of PQ.

By midpoint formula, the coordinates of point L are given by [(2 - 2)/2, (1 + 3)/2] = (0, 2)

Therefore, the equation of the line passing through points (4, 5) and (0, 2) is

y - 5 = (2 - 5)/(0 - 4) (x - 4)

y - 5 = (- 3)/(- 4) (x - 4)

4 (y - 5) = 3(x - 4)

4 y - 20 = 3x - 12

3x - 4 y + 8 = 0

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

NCERT Solutions Class 11 Maths Chapter 10 Exercise 10.2 Question 9

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

Summary:

The equation of the median of the ΔPQR with vertices P (2, 1), Q (- 2, 3) and R (4, 5) through vertex R is 3x - 4 y + 8 = 0