Construction – SS3 Mathematics Lesson Note (Second Term)

A locus is the path traced by a point that moves under one or more given conditions. The plural is loci. A locus can be the set of points at a fixed distance from a point, a line, or two points. This lesson covers four types of loci and how to construct each with a mathematical set.

Behavioural objectives

By the end of the lesson, students should be able to:

• define loci;
• state the types of loci;
• construct each type of locus;
• measure lines and angles correctly.

Instructional resource

Mathematical set.

What is a locus?

The locus of a point is the path traced by that point under a specific condition or conditions. The plural of locus is loci. It could be the distance from a point, a line, two points, etc.

Teacher’s activities: Explains the meaning of locus to the whole class.

Students’ activities: Note down the points.

What are the types of loci and how are they constructed?

The teacher leads the whole class through each construction. Students construct the same in their books.

1. Locus of a point equidistant from a fixed point

This is the circumference of a circle with the fixed point as the centre. For example, draw the locus of a point 2 cm from a fixed point.

2. Locus of a point equidistant from two fixed points

This is the perpendicular bisector of the line segment joining the two points. For example, construct the locus of a point equidistant from two points A and B, where |AB| = 7 cm.

3. Locus of a point equidistant from two intersecting straight lines

This is the pair of bisectors of the angles formed by the two lines.

4. Locus of a point at a fixed distance from a given straight line

This is two parallel lines, one on each side of the given line. For example, construct the locus of a point 3.2 cm from line AB.

Evaluation

The teacher asks the students the following questions, and the students respond.

1. Define loci.
2. State the locus of a point equidistant from two fixed points.
3. Construct the locus of a point 3 cm from a given point.

Assignment

• Construct a circle with a triangle inside.

References

• New General Mathematics for SS 1 by J B Channon et al.
• New Concept Mathematics for SS 1 by H N Odogwu et al.