Example 13 - Centroid of triangle ABC is (1, 1, 1) - Examples

  1. Chapter 12 Class 11 Introduction to Three Dimensional Geometry
  2. Serial order wise
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Example, 13 The centroid of a triangle ABC is at the point (1, 1, 1). If the coordinates of A and B are (3, –5, 7) and (–1, 7, – 6), respectively, find the coordinates of the point C. Let ABC be a triangle where A (3, –5, 7) , B( –1, 7, –6) Let G be the centroid of ∆ ABC So, G (1, 1, 1) Let Coordinate of C (x, y, z) We know that Co ordinate of centroid whose vertices are (x1 , y1 ,z1) ,(x2 ,y2 ,z2) (x3 ,y3 ,z3) is ﷐﷐﷐𝑥﷮1﷯ + ﷐𝑦﷮1﷯ + ﷐𝑧﷮1﷯﷮3﷯,﷐﷐𝑥﷮2﷯ + ﷐𝑦﷮2﷯ + ﷐𝑧﷮2﷯﷮3﷯,﷐﷐𝑥﷮3﷯ + ﷐𝑦﷮3﷯ + ﷐𝑧﷮3﷯﷮3﷯﷯ Here, x1 = 3 , y1 = –5 , z1 = 7 x2 = –1 , y2 = 7 , z2 = – 6 x3 = x , y2 = y , z3 = z ∴ Coordinates of G (1, 1, 1) = ﷐﷐3 + ﷐−1﷯ + 𝑥﷮3﷯,﷐−5 + 7 + 𝑦﷮3﷯,﷐7 + ﷐−6﷯ + 𝑧﷮3﷯﷯ (1, 1, 1) = ﷐﷐2 + 𝑥﷮3﷯,﷐2 + 𝑦﷮3﷯,﷐1 + 𝑧﷮3﷯﷯

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