Question

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

Answer 1

The given lines can be written as

$y=\frac{2}{3}x+\frac{1}{3}$ ... (1)

$y=-x+3$ ... (2)

$y=\frac{2}{3}x-\frac{2}{3}$ ... (3)

$y=-x+4$ ... (4)

The slope of lines (1) and (3) is $\frac{2}{3}$ 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, the given lines form a parallelogram.