Check sibling questions

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

Example 13 - Chapter 12 Class 11 Introduction to Three Dimensional Geometry - Part 2
Example 13 - Chapter 12 Class 11 Introduction to Three Dimensional Geometry - Part 3

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


Transcript

Example 9 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) x – coordinate 1 = (2 + 𝑥)/3 3(1) = 2 + x x = 1 y – coordinate 1 = (2 + 𝑦)/3 3(1) = 2 + y y = 1 z – coordinate 1 = (1 + 𝑧)/3 3(1) = 1 + z y = 2 Hence Required coordinate of C = (x, y, z) = (1, 1, 2)

Ask a doubt
Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.