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61. Prove that the points (4, 3), (6, 4), (5, 6) and (3, 5) are the vertices of aM. U. 82)square. |
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Answer» let ABCD be a quadrilateralwhere A(4,3);B(6,4)C(5,6) and D(3,5) are co ordinatesnow by section formula√((4-6)2+(3-4)2)=√((-2)2+(-1)2)=4+1=5.......(i)√((6-5)2+(4-6)2)=√((-1)2+(-2)2)=1+4=5......(ii) ⇒From (i)&(ii)we get AB = BC....(iii)similarly by section fomula AC=BD....(iv)So,we get that two adjacent sids are equal and two diagonals are equalHence, ABCD is a squareso points A,B,C,D are the angular points of a square.(Hence prooved) |
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