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

  1. Chapter 12 Class 11 Introduction to Three Dimensional Geometry
  2. Serial order wise

Transcript

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 1 + 1 + 1 3 , 2 + 2 + 2 3 , 3 + 3 + 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 + 3 , 5 + 7 + 3 , 7 + 6 + 3 (1, 1, 1) = 2 + 3 , 2 + 3 , 1 + 3

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