Question

101. The figure formed by the lines 2x–5y + 4 = 0,
5x + 2y + 7 = 0, 2x–5y + 3 = 0, 5x + 2y—6 = 0
is
1) Parallelogram 2) Rhombus
3) Rectangle
4) Square​

Answer 1

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Answer 2

Answer:

(3)The given lines form an Rectangle

Step-by-step explanation:

The given lines are

$L_{1} = 2x - 5y + 4 = 0 \\ L_{2} = 5x + 2y + 7 = 0 \\ L_{3} = 2x - 5y + 3 = 0 \\ L_{4} = 5x + 2y - 6 = 0$

The slopes of the lines are written as follows

$m_{1} = \frac{2}{5} \\ m_{2} = \frac{ - 5}{2} \\ m_{3} = \frac{2}{5} \\ m_{4} = \frac{ - 5}{2}$

Therefore,from the values of above slopes we can interpret that the lines 1 and 3 are parallel to each other,the lines 2 and 4 are parallel to each other,lines 1 and 2 are perpendicular to each other and same with lines 3 and 4.

Also the distance between two sets of parallel lines is unequal.

Therefore,the given lines form an Rectangle

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