Question

If P(2, 2), Q(- 2, 4) and R(3, 4) are the vertices of Δ PQR then the equation of the median through vertex R is ______.

पर्याय

• x + 3y + 9 = 0

• x - 3y + 9 = 0

• x - 3y - 9 = 0

• x + 3y - 9 = 0

Answer 1

If P(2, 2), Q(- 2, 4) and R(3, 4) are the vertices of Δ PQR then the equation of the median through vertex R is x - 3y + 9 = 0.

Explanation:

Mid-point of point P(2, 2) and Q(-2, 4) is

`((2 - 2)/2, (2 + 4)/2)`

i.e. (0, 3)

Required equation of median passing through vertex R is

`"y" - 4 = (3 - 4)/(0 - 3)`(x - 3)

`=> ("y" - 4) = 1/3 (x - 3)`

⇒ 3y - 12 = x - 3

⇒ x - 3y + 9 = 0