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.

Question

Philoid · Accepted Answer

Given: The coordinates of the A and B of the triangle ABC are (3, -5, 7) and (-1, 7, -6) respectively. The centroid of the triangle is (1, 1, 1)

To find: the coordinates of vertex C

Formula used:

Centroid of triangle ABC whose vertices are A(x₁, y₁, z₁), B(x₂, y₂, z₂) and C(x₃, y₃, z₃) is given by,

Here A(3, -5, 7) and B(-1, 7, -6)

Centroid of the triangle

On comparing:

⇒ 2 + x₃ = 3

⇒ x₃ = 3 – 2

⇒ x₃ = 1

⇒ 2 + y₃ = 3

⇒ y₃ = 3 – 2

⇒ y₃ = 1

⇒ 1 + z₃ = 3

⇒ z₃ = 3 – 1

⇒ z₃ = 2

Hence, coordinates of vertex C(1, 1, 2)