Q. 155.0( 3 Votes )

# Prove that the lines 2x – 3y + 1 = 0, x + y = 3, 2x – 3y = 2 and x + y = 4 form a parallelogram.

Answer :

__Given:__ 2x – 3y + 1 = 0,

x + y = 3,

2x – 3y = 2

x + y = 4 are given equation

To prove:

The lines 2x – 3y + 1 = 0, x + y = 3, 2x – 3y = 2 and x + y = 4 form a parallelogram.

Explanation:

The given lines can be written as

… (1)

… (2)

… (3)

… (4)

The slope of lines (1) and (3) is and that of lines (2) and (4) is − 1.

Thus, lines (1) and (3), and (2) and (4) are two pair of parallel lines.

If both pair of opposite sides are parallel then, we can say that it is a parallelogram.

Hence proved, the given lines form a parallelogram.

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