Question

Let PS be the median of the triangle with vertices P(2, 2), Q(6, – 1) and R(7, 3). The equation of the line passing through (1, – 1) and parallel to PS is

(a) 2x – 9y – 7 = 0

(b) 2x – 9y – 11 = 0

(c) 2x + 9y – 11 = 0

(d) 2x + 9y + 7 = 0

Answer 1

The correct option (d) 2x + 9y + 7 = 0

Explanation:

P(2, 2), Q(6, – 1) and R(7, 3) midpoint of Q(6, – 1) and R(7, 3) is [{(6 + 7)/2}, {(– 1 + 3)/2}] ≡ [(13/2), 1]

∴ slope of median through P is = [(1 – 2)/{(13/2) – 2}] = [(– 2)/9]

∴ equation of median through point P is

y + 1= [(– 2)/9](x – 1)

∴ 2x + 9y + 7 = 0