Question

. One vertex of an equilateral triangle is (2.2) and its centroid is(-2/√3,2/√3) then length of its is​

Answer 1

Answer: 4(2)^1/2

Step-by-step explanation:

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Answer 2

Concept

The centroid of a triangle is the centre most point of the triangle. If we measure it from any corner of the equilateral triangle  it is always equal.

Given

One vertex is (2,2) and the centroid is (-2/$\sqrt{3}$,2/$\sqrt{3}$)

To find

the length

Explanation

The length of the centroid from the vertex is $\sqrt{(2/\sqrt{3}-2)^{2} +(-2/\sqrt{3}-2)^{2} }$

=$\sqrt{4/\sqrt{3}+4-8/\sqrt{3}+4/3+4+8/\sqrt{3} }$

=$\sqrt{8/3+8}$

=$\sqrt{32/3}$

Hence the length is $\sqrt{32/3}$.

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