Question

The centroid of an equilateral triangle is (0, 0). If two vertices of the triangle lie on x + y = 2√2, then one of them will have its coordinates.

(a) (√2 + √6, √2 - √6)

(b) (√2 + √3, √2 - √3)

(c) (√2 + √5, √2 - √5)

(d) none of these

Answer 1

The correct option is (a).

Explanation:

Perpendicular distance of (0,0) from x+y−2√2 = 0 is given by:

For equilateral triangle, if height is h then:

Any point on line x+y−2√2 = 0 will be (h,2√2−h)

OC = 4

Using Shridaracharya's formula, we get:

Hence one of the vertex is (√2 + √6, √2 −√6).