Question

In a triangle ABC, A ≡ (0, 2), B ≡ (4, 0). If the centroid of the triangle lies on the locus y = x, then the equation of locus of the third vertex C is ______

Options

• y - x = 2

• x - y = 2

• y = x

• x + y = 2

Answer 1

In a triangle ABC, A ≡ (0, 2), B ≡ (4, 0). If the centroid of the triangle lies on the locus y = x, then the equation of locus of the third vertex C is y - x = 2.

Explanation:

Let (x, y) be the coordinate of point C and G (a, b) be the centroid.

Since G lies on the locus y = x

∴ b = a  .......................(i)

Also, a = `(0 + 4 + x)/3 = (x + 4)/3, b = (2 + 0 + y)/3 = (2 + y)/3`

Substituting the values of a and b in (i), we get

`(x + 4)/3 = (2 + y)/3`

⇒ >x + 4 = 2 + y

⇒ >y - x = 2