Zaymiey

📐 Mathematics  ·  Introduction to Three Dimensional Geometry  ·  JEE

If the origin is the centroid of a triangle with vertices (2a, 2, 6), (−4, 3b, −10) and (8, 14, 2c), then a, b and c are:

Answer: a = −2, b = −16/3, c = 2.

  • A a = −2, b = −16/3, c = 2
  • B a = 2, b = 16/3, c = −2
  • C a = −2, b = 16/3, c = −2
  • D a = 4, b = −5, c = 1

Correct answer: A. a = −2, b = −16/3, c = 2

Explanation: Setting each centroid coordinate to zero: 2a − 4 + 8 = 0 gives a = −2; 2 + 3b + 14 = 0 gives b = −16/3; 6 − 10 + 2c = 0 gives c = 2.

zxyOP(x, y, z)first octant:x>0, y>0, z>0

Concept context

Coordinate axes and planes in space, octants, distance between two points, and the section formula

Read the full Introduction to Three Dimensional Geometry notes →