Question

If G`(overlineg)` is the centroid, `H(overlineh)` is the orthocentre and P`(overlinep)` is the circumcentre of a triangle and `xoverlinep + yoverlineh + zoverlineg = 0`, then ______

Options

• x = 1, y = 2, z = -3

• x = -2, y = 5, z = 1

• x = 2, y = 1, z = -3

• x = 2,y = -3, z = 5

Answer 1

If G`(overlineg)` is the centroid, `H(overlineh)` is the orthocentre and P`(overlinep)` is the circumcentre of a triangle and `xoverlinep + yoverlineh + zoverlineg = 0`, then x = 2, y = 1, z = -3.

Explanation:

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

∴ `overlineg = (2.overlinep + 1.overlineh)/(2 + 1)`

⇒ `3overlineg = 2overlinep + overlineh`

⇒ `2overlinep + overlineh - 3overlineg = 0`

⇒ x = 2, y = 1, z = -3