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The locus of a point equidistant from two intersecting lines is 
  • a)
    A straight line
  • b)
    A circle
  • c)
    A pair of straight lines
  • d)
    None of the above
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The locus of a point equidistant from two intersecting lines isa)A str...

 
Let the intersection point be O and the point which is equidistant from the two lines be B
In triangle AOB and COB
AB = CB [∵ The point is equidistant]
OB is common
∠BAO = ∠BCO = 90° [Distance is measured along perpendicular]
∴ AOB ≅ COB
∠AOB = ∠COB
∴ The locus of all the points at the equidistant from the lines is the angular bisector of the lines
But since there are two pairs of vertically opposite angles made, there will two such angle bisector
∴ Locus is a pair of straight lines
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The locus of a point equidistant from two intersecting lines isa)A straight lineb)A circlec)A pair of straight linesd)None of the aboveCorrect answer is option 'C'. Can you explain this answer?
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