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coordinate plane problems portfolio 2024

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Creating a portfolio of coordinate plane problems for 2024 can be both educational and fun! Here are several types of problems that you can include, ranging in difficulty and covering various concepts related to the coordinate plane, such as plotting points, identifying slopes, analyzing equations of lines, calculating distances, and solving real-world applications.

Problem Set: Coordinate Plane Problems

Basic Problems

  1. Plotting Points:

    • Plot the following points on a coordinate plane: A(2, 3), B(-1, -4), C(0, 0), D(-3, 2).
    • Describe the location of each point in relation to the origin.

  2. Identifying Quadrants:

    • Determine which quadrant the following points are located in: E(-2, 5), F(4, -3), G(0, -2), H(-3, 0).

Intermediate Problems

  1. Finding the Distance Between Points:

    • Find the distance between the points P(3, 4) and Q(-1, -1) using the distance formula.

  2. Midpoint Calculation:

    • Calculate the midpoint of the segment connecting the points R(4, 6) and S(2, -2).

  3. Slope of a Line:

    • Find the slope of the line passing through the points T(1, 2) and U(4, 8).

Advanced Problems

  1. Equation of a Line:

    • Write the equation of the line in slope-intercept form that passes through point V(2, 3) with a slope of 5.

  2. Intersection of Lines:

    • Determine the intersection point of the lines given by the equations y = 2x + 3 and y = -3x + 1.

  3. Graphing Linear Equations:

    • Graph the equation 2x - y = 4. Identify the x-intercept and y-intercept.

Application Problems

  1. Real-world Application:

    • A park is located at the point (4, 7) on a coordinate plane. If a walking path starts at the origin (0, 0) and follows the line y = 1.5x, where will it intersect the path to the park?

  2. Area of a Triangle:

    • Find the area of a triangle whose vertices are at A(0, 0), B(6, 0), and C(3, 4).

Challenge Problems

  1. Distance from a Point to a Line:

    • Find the distance from the point D(1, 2) to the line given by the equation 3x - 4y + 5 = 0.

  2. Equation of a Perpendicular Line:

    • Given the line with the equation y = -2x + 5, find the equation of the line that is perpendicular to this line and passes through the point (2, 1).

Portfolio Presentation

  • Title Page: Include a title, your name, and the date.
  • Problem Sections: Organize the problems into sections (Basic, Intermediate, Advanced, Applications, Challenges).
  • Solutions: Provide detailed solutions to each problem, showing step-by-step calculations and reasoning.
  • Graphs: Incorporate visual elements such as graphs where applicable to enhance understanding.
  • Reflection: Write a brief reflection on what you learned through this project, what challenges you faced, and how you overcame them.

Conclusion

This portfolio will not only help you understand the concepts related to the coordinate plane but also develop problem-solving and analytical skills. Good luck with your portfolio for 2024!