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  4. One vertex of the equilateral triangle with centroid at the origin and one side as x + y - 2 = 0 is

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Q. 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:

[Hint : Let Let ABC be the equilateral triangle with vertex A(h, k) and let $D (\alpha, \beta)$ be the point on BC. Then $\frac{2 \alpha + h}{3} =0 = \frac{2 \beta + k}{3}$
Also $\alpha + \beta - 2 = 0 $ and $\left( \frac{ k - 0}{h -0}\right) \times (-1) = - 1 ] $