Question

If the origin is the centroid of the triangle whose vertices are \( A(2, p, -3) \), \( B(q, -2, 5) \) and \( C(-5, 1, r) \), then

• A. \( p = -1, q = 3, r = -2 \)
• B. \( p = 1, q = -3, r = -2 \)
• C. \( p = 1, q = 3, r = 2 \)
• D. \( p = 1, q = 3, r = -2 \)

Hint:

To find the coordinates of the centroid, take the average of the coordinates of the vertices of the triangle.

Answer 1

The Correct Option is D

Step 1: Use the centroid formula.
The centroid of a triangle is the average of the coordinates of its vertices. For the centroid to be at the origin, we must have: \[ \frac{2 + p + q + (-5)}{3} = 0, \quad \frac{p + (-2) + 1}{3} = 0, \quad \frac{-3 + 5 + r}{3} = 0 \] Step 2: Solve the system of equations.
Solving these equations, we find: \[ p = 1, \quad q = 3, \quad r = -2 \] Step 3: Conclusion.
The correct answer is (D) \( p = 1, q = 3, r = -2 \).