Question

If G(3, -5, r) is centroid of triangle ABC where A(7, - 8, 1), B(p, q, 5) and C(q + 1, 5p, 0) are vertices of a triangle then values of p, q, rare respectively.

Options

• 6, 5, 4

• -4, 5, 4

• -3, 4, 3

• -2, 3, 2

Answer 1

-2, 3, 2

Explanation:

The centroid of a triangle formed with vertices P(x₁, y₁, z₁), Q(x₂, y₂, z₂) and R(x₃, y₃, z₃) are

`((x_1 + x_2 + x_3)/3, ("y"_1 + "y"_2 + "y"_3)/3, ("z"_1 + "z"_2 + "z"_3)/3)`

Here, `((7 + "p" + "q")/3, (- 8 + "q" + 5"p")/3, (1 + 5 + 0)/3)` = (3, - 5, r)

`=> ((8 + "p" + "q")/3, (- 8 + 5"p" + "q")/3, 2)` = (3, - 5, r)

`=> (8 + "p" + "q")/3 = 3; (- 8 + 5"p" + "q")/3 = - 5; 2` = r

⇒ 8 + p + q = 9; - 8 + 5p + q = - 15; r = 2

⇒ p + q = 1; 5p + q = - 7; r = 2

⇒ p = - 2, q = 3, r = 2