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