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

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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**

**QUICK ANSWER…**

**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:**

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

**KEY-POINTS…**

**You may please note these/this:**

**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 20****21**** JAMB-UTME**** MATHEMATICS**** question**** 21 ****/**