# The locus of a point which moves so that it is equidistant…

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### Find the x - coordinate of a Point on a Line Given by its Equation

Find the x - coordinate of a Point ...
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## The locus of a point which moves so that it is equidistant from two intersecting straight lines is the?

A. perpendicular bisector of the two lines

B. angle bisector of the two lines

C. bisector of the two lines

D. line parallel to the two lines

B

## DETAILS…

The locus of a point which moves so that it is equidistant from two intersecting straight lines is the angle bisector of the two lines.

If two lines intersect, a third line can only be equidistant from the two lines if and only if the third line is a bisector of the angle between the two lines.

This third line is called the locus of a point which moves so that it is equidistant from two intersecting straight lines.

### Now for the right answer to the above question:

1. Option A is incorrect. there can be no single perpendicular bisector of the two lines.
2. Option B is correct. a third line which bisects the angle between the two lines is the locus.
3. C is incorrect. the term ‘bisector’ here is ambiguous, it is not clear what is being bisected, so this option is ignored.
4. D is not the correct answer. no one line can be simultaneously parallel to the two lines.
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## KEY-POINTS…

For the locus of a point,

• Equidistance simply means an equal distance.
• Locus is a path in construction mathematics that obeys a certain rule.
• Locus of a point which is equidistant from a point = a circle.
• Locus of a point which is equidistant from a straight line = another line parallel to the straight line.
• Locus of a point which is equidistant from two parallel lines = another parallel line at the center of the two parallel lines.
• Locus of a point which is equidistant from two intersecting straight lines = angle bisector of the two lines.

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/ culled from 2021 JAMB-UTME MATHEMATICS question 21 /