Question

If coordinates of vertices of a triangle are (7, 6, 4), (5, 4, 6), (9, 5, 8), find the coordinates of centroid of the triangle.

(a) (7, 5, 3)

(b) (7, 3, 5)

(c) (5, 3, 7)

(d) (3, 5, 7)

The question was asked in examination.

Question is from Three Dimensional Geometry in section Three Dimensional Geometry of Mathematics – Class 11

Answer 1

The correct answer is (a) (7, 5, 3)

Explanation: If coordinates of vertices of a triangle are (x1, y1, z1), (x2, y2, z2), (x3, y3, z3) the coordinates of centroid of the triangle are ((x1+x2+x3)/3, (y1+y2+y3)/3, (z1+z2+z3)/3)

So, coordinates of centroid of the given triangle are ((7+5+9)/3, (6+4+5)/3, (4+6+8)/3) = (7, 5, 3).