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Straight Lines — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSStraight Lines1 Mark
MCQ

The figure formed by the lines $\text{ax} \pm \text{by} \pm \text{c} = 0 $ is:

  • A
    a rectangle.
  • B
    a square.
  • C
    a rhombus.
  • D
    None of these.
✓

Answer

  1. a rhombus.

Solution:

 The given lines can be written separately in the following manner:

ax + by + c = 0 ...(1)

ax + by - c = 0 ...(2)

ax - by - c = 0 ...(3)

ax - by - c = 0 ...(4)

Graph of the given lines is given below:

Clearly, $\text{AB}=\text{BC}=\text{CD}=\text{DA}=\sqrt{\frac{\text{a}^2}{\text{c}^2}+\frac{\text{b}^2}{\text{c}^2}}=\frac{\sqrt{\text{a}^2+\text{b}^2}}{|\text{c}|}$

Thus, the region formed by the given lines is ABCD, which is a rhombus. 

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