Question

The centroid of the triangle with vertices A(2, -3, 3), B(5, -3, -4) and C(2, -3, -2) is the point
1. (-3, 3, -1)
2. (3, -3, -1)
3. (3, 1, -3)
4. (-3, -1, -3)
5. None of these

Answer 1

Correct Answer - Option 2 : (3, -3, -1)

Concept:

If A (x₁, y₁, z₁), B (x₂, y₂, z₂) and C (x₃, y₃, z₃) are the vertices of ΔABC. Then the centroid of ΔABC is given by: \(\left( {\frac{{{x_1} + {x_2} + {x_3}}}{3},\frac{{{y_1} + {y_2} + {y_3}}}{3},\frac{{{z_1} + {z_2} + {z_3}}}{3}} \right)\)

Calculation:

Given: The vertices of ΔABC are: A(2, -3, 3), B(5, -3, -4) and C(2, -3, -2)

As we know that, if A (x₁, y₁, z₁), B (x₂, y₂, z₂) and C (x₃, y₃, z₃) are the vertices of ΔABC. Then the centroid of ΔABC is given by: \(\left( {\frac{{{x_1} + {x_2} + {x_3}}}{3},\frac{{{y_1} + {y_2} + {y_3}}}{3},\frac{{{z_1} + {z_2} + {z_3}}}{3}} \right)\)

\(\Rightarrow \;\left( {\frac{{2 + 5 + 2}}{3},\frac{{ - \;3 - 3 - 3}}{3},\frac{{3 - 4 - 2}}{3}} \right) = \left( {3,\; - 3,\; - 1} \right)\)