InterviewSolution
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InterviewSolution
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If two vertices of an equilateral triangle have rational co-ordinates, then for the third vertex which one is most applicable?A. integral coordinatesB. coordinates which are rationalC. at lest one coordinate irrationalD. coordinates which are irrational |
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Answer» Correct Answer - C Let `A(x_(1),y_(1)),B (x_(2),y_(2))` and `Cx_(3),y_(3))` be the verticales of an equilateral triangle ABC such that `x_(1),x_(2)` and `y_(1),y_(2)` are integers. If we assume that none of the coordinates of the vertex C are irrational, then we find that `Delta = "Area of " Delta ABC` `rArr Delta = (1)/(2)|{:(,x_(1),y_(1),1),(,x_(2),y_(2),1),(,x_(3),y_(3),1):}|="A rationa number"` But, `Delta = (sqrt(3))/(4)("Side")^(2)=(sqrt(3))/(4) xx" A rational number"` `rArr " Delta = "An irrational number"` Thus , we are arrive at contradiction. Therefore, our supposition is worng . Hence, at lest one coordinate of C is irrational. |
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