InterviewSolution
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InterviewSolution
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If two adjacent vertices of a parallelogramare (3, 2) and (-1, 0) and the diagonals intersect at (2, -5), then find the coordinates of the other two vertices. |
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Answer» Solution :Let two ADJACENT vertices of a PARALLELOGRAM are `A-=(3, 2) and B(-1, 0).` Let coordinates of other two vertices are `C(x_(1), y_(1)) and D(x_(2),y_(2)).` We KNOW that diagonals of a parallelogram bisect each other. `therefore` Mid-point of AC and Mid-point of BD are same i.e., point O(2, -5). `therefore""(3+x_(1))/(2)=2 and (2+y_(1))/(2)=-5` `rArr""x_(1)=1 and y_(1)=-12 rArrC-=(x_(1), y_(1))-=(1, -12)` Also, `""(x_(2)-1)/(2)=2 and (y_(2)+0)/(2)=-5` `rArr""x_(2)=5 and y_(2)=-10rArrD-=(5, -10)` Hence,remaining vertices are (1, -12) and (5, -10). 
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