Question: COURSE WORK FOR GRADE XI SCIENCE Topic: COORDINATE GEOMETRY Purpose of the Course Work This project aims to help students: bullet apply coordinate geometry concepts to solve mathematical problems; bullet develop skills in using coordinates, gradients, distances and equations of lines; bullet connect coordinate geometry with real-life situations; bullet develop reasoning, communication and presentation skills; bullet compare different methods and interpret mathematical results. Learning Outcomes By completing this course work, students should be able to: bullet calculate the distance between two points; bullet determine the midpoint and coordinates of a point dividing a line segment; bullet calculate and interpret the gradient of a line; bullet find the equation of a straight line; bullet determine relationships between parallel and perpendicular lines; bullet apply coordinate geometry to real-life situations; bullet represent mathematical relationships using graphs and diagrams. Important Note on Original Work and Plagiarism All students are expected to produce their own original work for this course work. Each student must create their own mathematical questions, graphs, examples and real-life applications. No two students should submit exactly the same set of questions, graphical representation, numerical values or explanations. Copying questions, solutions, graphs or explanations from classmates or other sources without acknowledgement is not permitted. Students are encouraged to create their own mathematical problems based on concepts learned in class. Projects containing identical or highly similar work may lose marks under the Originality and Presentation criterion. PROJECT REQUIREMENTS Your project must contain ALL the following sections. Section 1 1 Introduction Include: bullet definition of coordinate geometry; bullet brief history/background of coordinate geometry; bullet importance and applications of coordinate geometry; bullet explanation of the Cartesian coordinate system; bullet brief explanation of the main concepts used in the project. Note: The introduction should be two pages or less. Section 2 1 Basic Concepts of Coordinate Geometry Create and solve at least: A. Distance Between Two Points bullet Create one problem involving two points. bullet Find the distance between the points using the distance formula. bullet Show all working steps. bullet Represent the points on a coordinate plane. B. Midpoint bullet Create one problem involving the midpoint of a line segment. bullet Find the midpoint using the midpoint formula. bullet Show the solution clearly. bullet Represent the points and midpoint graphically. C. Section Formula bullet Create one problem involving a point dividing a line segment in a given ratio. bullet Apply the section formula. bullet Interpret the answer on the coordinate plane. For EACH Problem: 1. Write the coordinates clearly. 2. State the appropriate formula. 3. Show all steps. 4. Give the final answer. 5. Include a suitable diagram or graph where appropriate. Section 3 1 Straight Lines Solve at least: A. Gradient of a Straight Line bullet Create one problem involving the gradient of a line. bullet Calculate the gradient using: bullet Interpret the meaning of the gradient. B. Equation of a Straight Line Create and solve at least two problems involving the equation of a straight line. Students may use: Point-slope form: or Slope-intercept form: y=mx + c Show all steps and draw the corresponding graph. C. Parallel and Perpendicular Lines Create and solve at least: bullet one problem involving parallel lines; bullet one problem involving perpendicular lines. Explain how the gradients can be used to determine whether two lines are parallel or perpendicular. Section 4 1 Real-Life Application Create TWO real-life situations involving coordinate geometry. Your task should include: bullet problem statement; bullet mathematical model; bullet appropriate coordinates; bullet formula or method used; bullet complete solution; bullet graph/diagram; bullet explanation and interpretation of the answer in context. Possible Contexts Students may choose situations involving: bullet mapping and navigation; bullet road networks; bullet architectural design; bullet construction; bullet land measurement; bullet location of buildings; bullet sports fields; bullet transportation routes; bullet distances between places; bullet computer graphics; bullet GPS and digital maps. Students should create their own situations rather than copying examples from textbooks or the internet. Section 5 1 Reflection and Conclusion Students should reflect on: bullet Which coordinate geometry concept was easiest and why? bullet Which concept was most difficult? bullet Which formula or method was most useful? bullet How is coordinate geometry useful in real life? bullet What did you learn from completing the project? bullet How did drawing graphs help you understand coordinate geometry? bullet What challenges did you face and how did you overcome them? Conclude the project by summarising the importance of coordinate geometry in mathematics and everyday life. PRESENTATION AND ORGANIZATION The project should include: bullet neat layout; bullet correct mathematical notation; bullet clearly labelled graphs; bullet appropriate use of diagrams; bullet proper explanation; bullet creativity and organization; bullet correct use of units where applicable; bullet clearly numbered sections and questions. SUBMISSION FORMAT Students may choose any ONE of the following formats: Option 1 1 Written Report Traditional notebook/file project containing all required sections, calculations, graphs and explanations. Option 2 1 Digital Slide Presentation Students may use: bullet PowerPoint; bullet Google Slides; bullet Canva; bullet other appropriate digital presentation tools. The presentation should contain mathematical explanations, graphs, diagrams and solutions. Option 3 1 Video Explanation Students record themselves teaching or explaining the coordinate geometry concepts and solutions. The video should clearly demonstrate: bullet mathematical concepts; bullet solution methods; bullet graphs/diagrams; bullet explanation of real-life applications. COURSE WORK RUBRIC 1 COORDINATE GEOMETRY Criteria Excellent Good Satisfactory Needs Improvement Marks 1. Accuracy 9 6 marks: All calculations, formulas, graphs and solutions are correct and complete. Work is carefully checked and mathematical notation is accurate. 7 8 marks: Most calculations and solutions are correct, with only minor errors. Graphs and notation are mostly accurate. 5 6 marks: Some solutions are correct, but several errors are present. Understanding is partially demonstrated. 1 4 marks: Many errors are present. Solutions are incomplete or incorrect, showing limited understanding. /10 2. Use of Required Methods 7 8 marks: Correctly applies required coordinate geometry formulas and methods, including distance, midpoint, section formula, gradient and equation of a line. Shows strong understanding of when and how methods are used. 5 6 marks: Most required methods are used correctly, with minor errors or incomplete explanations. 3 4 marks: Some required methods are used correctly, but there are noticeable mistakes or missing methods. 1 2 marks: Very limited or incorrect use of required methods. Important methods are missing or misapplied. /8 3. Real-Life Application 9 10 marks: Real-life situations are highly relevant, realistic and creative. Mathematical models are clearly developed and solutions are thoroughly explained and interpreted. 7 8 marks: Real-life applications are relevant and mostly realistic. Mathematical models and explanations are clear. 5 6 marks: Basic real-life application is included but may lack depth, clarity or creativity. 1 4 marks: Real-life application is weak, unrealistic or incomplete. Little or no meaningful connection to coordinate geometry is shown. /10 4. Explanation and Reasoning 4 marks: Explanations are clear, logical and detailed. Mathematical reasoning is accurate and consistently demonstrated. 3 marks: Explanations are mostly clear and logical. Some mathematical reasoning is demonstrated. 2 marks: Explanations are limited or partially unclear. Reasoning is sometimes incomplete. 1 mark: Very little explanation or reasoning is provided. Mathematical thinking is unclear or missing. /4 5. Organizatio n, Presentation and Originality 4 marks: Project is exceptionally neat, well-organized and creative. Graphs and diagrams are clearly labelled. Work is visually appealing and original. 3 marks: Project is organized and neat with mostly clear graphs and diagrams. Some originality is shown. 2 marks: Project is organized but may lack creativity or have some presentation problems. 1 mark: Project is poorly organized and difficult to follow. Graphs/diagrams are missing, unclear or copied. /4 6. Completion 4 marks: Project is submitted on time with all required sections completed. 3 marks: Project is submitted within one day after the deadline or has only minor missing components. 2 marks: Project is submitted within two days after the deadline or has some incomplete sections. 1 mark: Project is submitted three or more days late or major sections are missing. /4 Total: 40 Marks Submission Date: 5/10/2026 Suggested Student Checklist Before submission, students should ensure that their project contains: Introduction to coordinate geometry Cartesian coordinate system Distance formula problem Midpoint problem Section formula problem Gradient problem Equation of a straight-line problems Parallel and perpendicular line problems Clearly labelled graphs Two real-life applications Mathematical models and solutions Interpretation of real-life answers Reflection Conclusion Proper presentation and organization Original work

1. **Problem Statement:** Calculate the distance between two points $A(3,4)$ and $B(7,1)$ using the distance formula. 2. **Formula:** The distance $d$ between two points $A(x_1,y_1)$ and $B(x_2,y_2)$ is given by: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ 3. **Substitute the coordinates:** $$d = \sqrt{(7 - 3)^2 + (1 - 4)^2}$$ 4. **Calculate the differences:** $$d = \sqrt{4^2 + (-3)^2}$$ 5. **Square the differences:** $$d = \sqrt{16 + 9}$$ 6. **Sum the squares:** $$d = \sqrt{25}$$ 7. **Find the square root:** $$d = 5$$ 8. **Interpretation:** The distance between points $A$ and $B$ is $5$ units. 9. **Graphical Representation:** Plot points $A(3,4)$ and $B(7,1)$ on the coordinate plane and draw the line segment connecting them to visualize the distance.