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The base f an equilateral triangle with ...

The base f an equilateral triangle with side `2a` lies along the y-axis such that the mid point of the base is at the origin. Find the vertices of the triangle.

Text Solution

Verified by Experts

Since, O is the mid- point of baic BC of length `2a`.
therefore,
`OB=OC=a`
Also, since it is equilateral triangle, therefore
Now, by Pythagoras theorem,
`AB^2=OA^2+OB^2`
`rArrOA^2=AB^2-OB^2`
`=(2a)^(2)-a^2=3a^2`
`thereforeOA=sqrt(3a^(2))=asqrt(3)`
`therefore A=(asqrt(3,0), B=(0,a)C=(0,-a)`
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