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$The number of equilateral triangles with y = \sqrt{3} (x - 1) + 2 and y = - x as two of its sides is$

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Correct option is D

The sides given are y=3(x−1)+2 and y=−x . Lines are at an angle 600 to each other. Now any line parallel to obtuse angle bisector will make equilateral triangle with these lines as its two sides.Therefore, infinitely many lines.

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The number of equilateral triangles with y=3(x−1)+2 and y=−x as two of its sides is

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$The number of equilateral triangles with y = \sqrt{3} (x - 1) + 2 and y = - x as two of its sides is$