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Question
One vertex of the equilateral triangle with centroid at the origin and one side as x+y−2=0 is
One vertex of the equilateral triangle with centroid at the origin and one side as x+y−2=0 is
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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+b−2=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,
h−ak−b×(−1)=−1
h−a=k−b
3a=3b
a=b=1
So, h=−2
and k=−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+b−2=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,
h−ak−b×(−1)=−1
h−a=k−b
3a=3b
a=b=1
So, h=−2 and k=−2.
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