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Question

One vertex of the equilateral triangle with centroid at the origin and one side as x+y2=0 is

A
(1,1)
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B
(2,2)
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C
(2,2)
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D
Non4 of these
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Solution

The correct option is C (2,2)

As the triangle is equilateral and the centroid is given at the origin, then it is also he orthocenter and AD is also the altitude where G divides it in the ratio 2:1.

As the point D(a,b) lies on BC, then

a+b2=0

If A is the point (h,k), then,

2a+h3=0 and 2b+k3=0

h=2a and k=2b

As AD is perpendicular to BC,

hakb×(1)=1

ha=kb

3a=3b

a=b=1

So, h=2 and k=2.


976120_1007056_ans_e41cd55deec04ab7a5a4cfdac3d6a516.png

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