Further Mathematics - Senior Secondary 1 - Coordinate Geometry (The Straight Line II)

Coordinate Geometry (The Straight Line II)

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TERM: 1ST TERM

WEEK 6
Class: Senior Secondary School 1
Age: 15 years
Duration: 40 minutes of 4 periods
Subject: Further Mathematics
Topic: Coordinate Geometry (The Straight Line II)
Focus:
i. Conditions for Parallelism and Perpendicularity
ii. Equation of a Line

SPECIFIC OBJECTIVES

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

  1. State and explain the condition for parallelism between two lines.
  2. State and explain the condition for perpendicularity between two lines.
  3. Derive the equation of a line using point-slope and two-point forms.
  4. Apply the derived forms to solve problems involving equations of straight lines.

INSTRUCTIONAL TECHNIQUES

  • Question and answer
  • Guided derivation
  • Class discussion
  • Practice exercises
  • Use of visual aids and charts

INSTRUCTIONAL MATERIALS

  • Whiteboard and markers
  • Charts showing different forms of line equations
  • Graph sheets
  • Ruler and graph boards
  • Worksheets on parallel and perpendicular lines

PERIOD 1 & 2: Conditions for Parallelism and Perpendicularity

PRESENTATION

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction

Reviews concept of gradient (slope) from previous lessons.

Students recall and share gradient definitions.

Step 2 - Parallel Lines

Explains that two lines are parallel if their gradients are equal (m₁ = m₂). Provides examples.

Students observe and note examples of parallel lines.

Step 3 - Perpendicular Lines

Explains that two lines are perpendicular if the product of their gradients is -1 (m₁ × m₂ = -1). Provides algebraic and graphical demonstrations.

Students solve simple gradient exercises to test perpendicularity.

Step 4 - Real-life Connection

Gives real-world applications, e.g., design of perpendicular roads, parallel railway tracks.

Students relate the math to physical observations.

NOTE ON BOARD

  • Parallel Lines: m₁ = m₂
  • Perpendicular Lines: m₁ × m₂ = -1

 

EVALUATION (5 exercises)

  1. What is the condition for two lines to be parallel?
  2. If line A has gradient 3, what must be the gradient of line B for it to be parallel to A?
  3. What is the condition for two lines to be perpendicular?
  4. If m₁ = 2, find m₂ for perpendicularity.

Are lines with gradients -2 and ½ perpendicular? Justify your answer.