Geometry

1. Coordinate Geometry
   1. Cartesian Coordinate System
      1. Definition and Origin
         1. Rectangular coordinate system representation
         2. Relation to graphs in two and three dimensions
      2. Axes and Quadrants
         1. X-axis and Y-axis
         2. Identification of four quadrants
         3. Sign conventions for each quadrant
      3. Points in a Plane
         1. Representation as ordered pairs (x, y)
         2. Plotting points on the Cartesian plane
         3. Understanding positive, negative, and zero coordinates
   2. Graphing Lines and Shapes
      1. Basics of Graphing
         1. Plotting linear equations
         2. Identifying points of intersection
      2. Graphing Linear Equations
         1. Slope-intercept form (y = mx + b)
         2. Standard form (Ax + By = C)
         3. Point-slope form (y - y₁ = m(x - x₁))
      3. Graphing Shapes
         1. Circles
            1. General equation (x - h)² + (y - k)² = r²
            2. Center-radius form
         2. Parabolas, ellipses, and hyperbolas
            1. Basic forms and characteristics
            2. Vertex, foci, and directrix concepts
   3. Equations of Shapes
      1. Line Equations
         1. Understanding different forms (slope-intercept, point-slope, and standard forms)
         2. Conversion between forms
         3. Parallel and perpendicular lines criteria
      2. Circle Equations
         1. Deriving the standard circle equation
         2. Applications involving tangent lines
         3. Completing the square to find circle properties
   4. Distance and Midpoint Formulas
      1. Distance Formula
         1. √((x₂ - x₁)² + (y₂ - y₁)²)
         2. Deriving and applying in different contexts
      2. Midpoint Formula
         1. ((x₁ + x₂)/2, (y₁ + y₂)/2)
         2. Use in finding center points
         3. Application in line segment division
   5. Slope and Intercept
      1. Slope Concept
         1. Definition as the rate of change
         2. Calculation using (y₂ - y₁) / (x₂ - x₁)
         3. Positive, negative, zero, and undefined slopes
      2. Y-intercept and X-intercept
         1. Finding intercepts algebraically
         2. Graphical interpretation
         3. Solving intercept problems in linear equations
      3. Applications of Slope
         1. Real-world applications (e.g., incline, rate of growth)
         2. Connection to calculus through derivatives