Lesson Notes By Weeks and Term v4 - SHS 2

Lesson Video

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Performance objectives

• Define the concept of a locus.
• Explain the relationship between tangent and normal lines.
• Derive the equation of a normal to a curve under specific conditions.
• Solve problems involving the equations of normal lines.

Lesson summary

In our daily lives, we see paths and boundaries everywhere. The curve of the road from Accra to Cape Coast, the circular ripple when a stone is dropped in the Kpeshie Lagoon, or the perfect circle drawn by an artist using a compass. All these are examples of a "locus." In mathematics, a locus is simply a set of points that follows a specific rule or condition. In this lesson, we will learn how to translate these geometric rules into the language of algebra to find their equations. This skill is fundamental in fields like engineering, architecture, and even in mobile phone technology (GPS).

Lesson notes

This lesson is about turning a description of a path into a mathematical equation. We will use our knowledge of coordinate geometry to do this. A. What is a Locus?

A locus (plural: loci) is a set of all points that satisfy a given geometric condition or rule. Think of it this way: Imagine a goat tied to a peg in a field with a rope 3 metres long. The goat can move anywhere as long as the rope is tight. What path will it trace on the ground? It will trace a perfect circle. The locus is the circle. The condition is that the goat must always be exactly 3 metres from the peg.

In the Cartesian plane, we represent a general point on the locus as P(x, y). Our goal is to find an equation that connects *x* and *y* based on the given rule. B. The Main Tool: The Distance Formula

Almost all locus problems in coordinate geometry depend on the distance formula. It helps us calculate the distance between any two points.

Evaluation guide

• Deduce relations of various loci under given conditions.
• Experiential Learning, Collaborative Learning, Talk for Learning and building on what others say.
• conceptual
• and reasoning