InterviewSolution
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InterviewSolution
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If two vertices of an equilaterla triangle have integral coordinates, then the third vetex will haveA. integral coodinates which are rtionalB. coordinates which are rationalC. at least one coordinate irrationalD. coordinates which are irrational |
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Answer» Correct Answer - C Let `A(x_(1),x_(2))B(x_(2),y_(2)) and C(x_(3),y_(3))` be the vertice of an equlateral 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 `DeltaABC` `rArr Delta=(1)/(2)|{:(x_(1),y_(1),1),(x_(2),y_(2),1),(x_(3),y_(3),1):}|=A` rational number But, `Delta=(sqrt(3))/(4) ("Side")^(2)=(sqrt(3))/(4)xxA` rational number `rArr Delta`= an irrational number Thus, we arrive at a conradinte. Therefore , our supposition is wrong Hence, at least at least one coordinate of C is irrational. |
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