Please help with locus problem

[jimi]

Problem is as follows:


O-----------------------A
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B|

'Draw accurately, on the diagram above, the locus of points which are the same distance from the line OA and the line OB'
(The lines OA and OB are the same length and they are perpendicular to each other).

 

[Guest]

the locus of points is the angle bisector of angle O

 

[jimi]

Thanks for reply. However, I always understood the distance of a point from a line is the perpendicular distance so is there another line that satisfies the locus which is perpendicular to the bisector of angle O and goes through O?

 

[Guest]

No,that's not possible. If u have another line perpendicular to angle bisector of angle O and goes through O, there is only pt O which satisfies the locus.
U can check by picking any point on the line and measure the distance from that pt to pt A and pt B.

 

[jimi]

'U can check by picking any point on the line and measure the distance from that pt to pt A and pt B.'

I understand what you're saying and I'm pretty sure that your interpretation is the answer. If the 2 lines were extended then there would be two bisectors. The difference is whether we are looking at line segments (as in this problem) or infinite lines.
Thanks for your replies.