Lesson 2.6 - Using Coordinates to Solve Problems

  • Lesson 2.6 - Using Coordinates to Solve Problems

    Learning Goals: By the end of this lesson you will be able to

    Use properties of lines and line segments to solve problems.

    • Review of Chapter 1, 2; Linear Systems and Analytic Geometry Assignment

      Review of: 
      Chapter 1: System of Linear Equations
      Chapter 2: Analytic Geometry

      Questions types: 

      1. a. Solve for x, given y = 89, equation y = 3x - 2
           b. What is y, if x = 50, given y = 3x - 2
      2. Find a Midpoint using the equation: M(x, y) = ( ( x1 + x2) / 2, (y1 + y2) / 2)); 
          Given A(4, 4), B(0, 0)
      3.  Give another equation that is parallel to y = 2x + 3,
      4. Name the type of Triangle that has two angles or two sides that are the same?
      5. Calculate the Length of a line segment using the Pythagorean Theorem and points P(3,2), Q(6,6)
      6. Find the equation of a line perpendicular (90 degrees) to y = x. 

      File: Chapter 1_and_2_review_20210924.pdf


    • Assignment #5 - Analytic Geometry - Lines, Circles and other shapes

      The student will be assessed on the following topics in rubrics format as stated below: 

      Knowledge and Understanding - 25%
      Thinking and Inquiry - 25%
      Communication - 25%
      Application - 25%

      Specific Expectations:
      2.1 Midpoint of a Line Segment
      2.2 Length of a Line Segment
      2.3 Equation of a Circle
      2.4 Classifying Figures on a Coordinate Grid
      2.5 Verifying Properties of Geometric Figures (Right Bisector of a Triangle, etc.)
      2.6 Exploring Properties of Geometric Figures (Centroid of Triangle, etc.)
      2.7 Using Coordinates to Solve Problems

      Key Terms:
      1. Slopes of Lines
      2. Parallel lines
      3. Perpendicular bisector
      4. Length of Line Segment
      5. Length of a hypotenuse
      6. Pythagorean Theorem
      7. Equation of a circle
      8. Point on a circle
      9. Median of a Triangle
      10. Equidistance
      11. Cartesian Grid
      12. Midpoint
      13. Altitude
      14. Radius of a Circle
      15. Fractal
      16. centroid
      17. Parallelogram
      18. Varignon Parallelogram
      19. Right-angle Triangle
      20. Isosceles Triangle
      21. Scalene Triangle
      22. Equilateral Triangle

    • Assignment #6 - Analytic Geometry: Advanced Shapes and Their Properties

      The student will be assessed on the following topics in rubrics format as stated below: 

      Knowledge and Understanding - 25%
      Thinking and Inquiry - 25%
      Communication - 25%
      Application - 25%

      Specific Expectations:
      2.1 Midpoint of a Line Segment
      2.2 Length of a Line Segment
      2.3 Equation of a Circle
      2.4 Classifying Figures on a Coordinate Grid
      2.5 Verifying Properties of Geometric Figures (Right Bisector of a Triangle, etc.)
      2.6 Exploring Properties of Geometric Figures (Centroid of Triangle, etc.)
      2.7 Using Coordinates to Solve Problems

      Key Terms:
      1. Slopes of Lines
      2. Parallel lines
      3. Perpendicular bisector
      4. Length of Line Segment
      5. Length of a hypotenuse
      6. Pythagorean Theorem
      7. Equation of a circle
      8. Point on a circle
      9. Median of a Triangle
      10. Equidistance
      11. Cartesian Grid
      12. Midpoint
      13. Altitude
      14. Radius of a Circle
      15. Fractal
      16. centroid
      17. Parallelogram
      18. Varignon Parallelogram
      19. Right-angle Triangle
      20. Isosceles Triangle
      21. Scalene Triangle
      22. Equilateral Triangle