Question

If the orthocentre and circumcentre of a triangle are (-3, 5, 1) and (6, 2, -2) respectively, then its centroid is ______

Options

• (1, 3, 3)

• (3, 3, -1)

• (6, -2, 3)

• (6, -2, -5)

Answer 1

If the orthocentre and circumcentre of a triangle are (-3, 5, 1) and (6, 2, -2) respectively, then its centroid is (3, 3, -1).

Explanation:

Let the coordinates of the centroid be (x, y, z).

Co-ordinates of orthocentre and circumcentre are (-3, 5, 1) and (6, 2, -2) respectively.

We know that centroid of the triangle divides the line segment joining its orthocentre and circumcentre in the ratio 2 : 1.

∴ (x, y, z) ≡ `((2(6) + 1(-3))/(2 + 1), (2(2) + 1(5))/(2 + 1), (2(-2) + 1(1))/(2 + 1))`

⇒ (x, y, z) ≡ (3, 3, -1)