Loci — Part 1: Circles, parallels and the perpendicular bisector: visual lesson, ICSE Class 10 Mathematics

Lesson

Loci, Part 1

A locus is the path of a point that obeys a rule. In this part we meet three loci you will draw again and again: the circle, the pair of parallel lines and the perpendicular bisector.

In this lesson you will

Explain what a locus is and describe a locus in words
Draw the locus of points at a fixed distance from a point (a circle) and from a line (two parallel lines)
Draw the perpendicular bisector as the locus of points equidistant from two points and use it to find lengths
Check, with distances, whether a point is on a given locus

Points at the same distance from $O$ lie on a circle: the locus.

Concept

What you will be able to do

Say what a locus is
Draw the locus at a fixed distance from a point or a line
Draw the perpendicular bisector of a segment
Test whether a point is on a locus

Concept

What is a locus?

A locus is the set of all the points, and only those points, that obey a given rule. It can be a curve, a line, a pair of lines or a region.

every point of the locus obeys the rule
every point that obeys the rule is on the locus
a locus is drawn, not just described: use a ruler and a pair of compasses

A locus is the path a point follows when it obeys a rule.
Situation	Condition on the moving point	Locus
tip of a minute hand, $7$ cm long	always $7$ cm from the pivot	a circle of radius $7$ cm
centre of a coin rolling along a ruler edge	always $1.5$ cm from the edge	a line parallel to the edge
a shelter equally far from two bus stops	same distance from both stops	the perpendicular bisector of the stops
a lamp equally far from two crossing roads	same distance from both roads	the two angle bisectors

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