Coordinate Geometry II

Grade 12 · Mathematics

Semester 1 | Period 3 | Week 16

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Subject: Mathematics

Semester: 1

Period: 3

Week: 16

WEEK 16

Class: Grade 12
Age: 17 years
Duration: 40 minutes of 5 periods
Subject: Mathematics
Topic: Coordinate Geometry II
Focus: Gradient of a straight line and y-intercept, Equation of a straight line, Angle between two intersecting lines, Condition for parallel lines and perpendicular lines, Practical application of coordinate geometry.

SPECIFIC OBJECTIVES:

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

  1. Define and calculate the gradient of a straight line.
  2. Define and calculate the y-intercept of a straight line.
  3. Write the equation of a straight line.
  4. Calculate the angle between two intersecting straight lines.
  5. Identify the condition for parallel lines and perpendicular lines.
  6. Apply the concept of coordinate geometry to real-life situations.

 

INSTRUCTIONAL TECHNIQUES:

  • Direct instruction
  • Group discussions
  • Problem-solving exercises
  • Guided practice
  • Real-life applications

 

INSTRUCTIONAL MATERIALS:

  • Graph board
  • Graph books
  • Graph charts

 

       5. If the equation of a line is y=−x+4, find its gradient and y-intercept.

 

PERIOD 3 & 4: Equation of a Straight Line

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction

Explains the formula for the equation of a straight line: y=mx+c. Explains how to derive the equation using given points or gradient and y-intercept.

Students pay attention and take notes on the equation of a straight line.

Step 2 - Deriving Equation

Works through examples with given coordinates to derive the equation of a straight line. For example, using the gradient and a point on the line to find the equation.

Students observe the process and participate in solving an example.

Step 3 - Guided Practice

Provides exercises for students to derive the equations of lines from different forms, including using the gradient and a point.

Students practice deriving equations individually and in pairs.

NOTE ON BOARD:
Equation of a line: y=mx+c, where m is the gradient and c is the y-intercept.

 

EVALUATION (5 exercises):

  1. Derive the equation of the line with gradient 3 and passing through the point (1,2).
  2. Write the equation of the line passing through points (2,4) and (5, 10).
  3. Find the equation of a line with gradient -2 passing through the point (3,6).
  4. What is the equation of the line with gradient 5 and passing through the point (1,2)?
  5. Write the equation of the line passing through points (0,4) and (3, 7).

CLASSWORK (5 questions):

  1. Derive the equation of the line with gradient 1 and passing through the point (4,6).
  2. Write the equation of the line with gradient -3 and passing through the point (2,5).
  3. What is the equation of the line through points (1,3) and (2, 5)?
  4. Find the equation of the line with gradient 0 and passing through (2,3).
  5. Write the equation of the line with gradient 4 passing through the point (0,−1).

ASSIGNMENT (5 tasks):

  1. Find the equation of the line with gradient 2 passing through the point (1,5).
  2. Write the equation of the line with gradient -1 and passing through the point (2,3).
  3. What is the equation of the line passing through (0,1) and (3, 7)?
  4. Derive the equation of a line with gradient 4 and passing through the point (3,5).
  5. Write the equation of the line passing through the points (1,2) and (4, 8).

 

PERIOD 5: Angle Between Two Intersecting Lines and Application

PRESENTATION:

  1. Calculate the angle between two lines with gradients 1 and -2.
  2. What is the angle between lines with gradients 0 and 1?
  3. Find the angle between two lines with gradients -3 and 2.
  4. If two lines have gradients 1/2 and 3/4, what is the angle between them?
  5. Calculate the angle between two lines with gradients 2 and 5.

ASSIGNMENT (5 tasks):

  1. Find the angle between lines with gradients 1 and 2.
  2. Calculate the angle between two lines with gradients -2 and 4.
  3. What is the angle between two lines with gradients 1/3 and -1/2?
  4. Calculate the angle between two lines with gradients 2 and -3.
  5. Provide a real-life scenario where the angle between two intersecting lines is important.