Q. 155.0( 4 Votes )
Prove that the lines 
, 
, 
and 
form a rhombus.
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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