Q. 154.4( 5 Votes )

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Answer :

Given: lines are as follows:


To prove:


lines form a rhombus.


Assuming:


In quadrilateral ABCD, let equations (1), (2), (3) and (4) represent the sides AB, BC, CD and


DA, respectively.


Explanation:


Lines (1) and (3) are parallel and lines (2) and (4) are parallel.


Solving (1) and (2):


x = 0, y = 0.


Thus, AB and BC intersect at B (0, 0).


Solving (1) and (4):


x , y


Thus, AB and DA intersect A


Solving (3) and (2):


x , y =


Thus, BC and CD intersect at C


Solving (3) and (4):


x , y


Thus, DA and CD intersect at D


Let us find the lengths of sides AB, BC and CD and DA.


AB


BC


CB


DA = 1


Hence Proved, the given lines form a rhombus.


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