Question

Perimeter of an equilateral triangle whose one vertex is at origin and centroid at (1, 7) is equal to :

Answer 1

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,

3

2a+h

=0 and

3

2b+k

=0

h=−2a and k=−2b

As AD is perpendicular to BC,

k−b

h−a

×(−1)=−1

h−a=k−b

3a=3b

a=b=1

So, h=−2 and k=−2.

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Answer 2

Answer:

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