Question
Download Solution PDFThe centroid of the triangle with vertices A(2, -3, 3), B(5, -3, -4) and C(2, -3, -2) is the point
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
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: \(\left( {\frac{{{x_1} + {x_2} + {x_3}}}{3},\frac{{{y_1} + {y_2} + {y_3}}}{3},\frac{{{z_1} + {z_2} + {z_3}}}{3}} \right)\)
\(\Rightarrow \;\left( {\frac{{2 + 5 + 2}}{3},\frac{{ - \;3 - 3 - 3}}{3},\frac{{3 - 4 - 2}}{3}} \right) = \left( {3,\; - 3,\; - 1} \right)\)Last updated on Jul 7, 2025
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