Linear & Coordinate Geometry
Linear & Coordinate Geometry
Linear & Coordinate Geometry
what you'll learn
Lesson details
Units 1 & 2 (Linear and Coordinate Geometry)
Focus on developing algebraic and graphical understanding of linear relationships, interpreting and constructing equations from geometric contexts, and working fluently with gradient, distance, midpoint, and parallel/perpendicular lines in the Cartesian plane. Introduces basic proof techniques using algebra and coordinates.
Unit 1: Linear Relationships and Cartesian Geometry
1.1 Linear Equations and Graphs
Form of Linear Equations: gradient-intercept form (y = mx + c), point-gradient form, general form (Ax + By + C = 0).
Gradient: interpreting as rate of change, calculating from two points.
Graphing Techniques: plotting using intercepts, gradient and point, or technology.
Contextual Applications: e.g. cost/revenue models, constant rate scenarios.
1.2 Parallel and Perpendicular Lines
Parallel Lines: identical gradients; solving geometric problems using this property.
Perpendicular Lines: product of gradients = –1; proving relationships between lines.
Intersecting Lines: solving simultaneous linear equations algebraically and graphically.
1.3 Distance and Midpoint Formulae
Distance: derived from Pythagoras’ Theorem, applied to two points in the plane.
Midpoint: average of coordinates, used in bisector and triangle centre problems.
Application to Geometric Proofs: e.g. proving triangle properties like isosceles, right-angled.
Unit 2: Coordinate Geometry and Introduction to Geometric Proof
2.1 Coordinate Geometry in Problem Solving
Modelling Figures with Coordinates: placing triangles, quadrilaterals, and other shapes in the plane for analysis.
Using Algebra to Justify Geometric Properties: congruence, parallelism, perpendicularity, equal length.
Area of Plane Figures: triangle and polygon area using determinant or formula-based methods.
2.2 Line Segments and Geometric Reasoning
Dividing Line Segments: internal division in a given ratio.
Collinearity and Concurrent Lines: establishing conditions using coordinates.
Use of Coordinate Geometry in Proofs: combining distance, gradient, and midpoint results to verify claims.
2.3 Applications and Modelling Contexts
Applied Geometry: e.g. designing structures with perpendicular supports, checking safety margins with distance constraints.
Interpretation of Geometric Models: understanding and analysing location-based or motion-related scenarios using linear equations.
Units 1 & 2 (Linear and Coordinate Geometry)
Focus on developing algebraic and graphical understanding of linear relationships, interpreting and constructing equations from geometric contexts, and working fluently with gradient, distance, midpoint, and parallel/perpendicular lines in the Cartesian plane. Introduces basic proof techniques using algebra and coordinates.
Unit 1: Linear Relationships and Cartesian Geometry
1.1 Linear Equations and Graphs
Form of Linear Equations: gradient-intercept form (y = mx + c), point-gradient form, general form (Ax + By + C = 0).
Gradient: interpreting as rate of change, calculating from two points.
Graphing Techniques: plotting using intercepts, gradient and point, or technology.
Contextual Applications: e.g. cost/revenue models, constant rate scenarios.
1.2 Parallel and Perpendicular Lines
Parallel Lines: identical gradients; solving geometric problems using this property.
Perpendicular Lines: product of gradients = –1; proving relationships between lines.
Intersecting Lines: solving simultaneous linear equations algebraically and graphically.
1.3 Distance and Midpoint Formulae
Distance: derived from Pythagoras’ Theorem, applied to two points in the plane.
Midpoint: average of coordinates, used in bisector and triangle centre problems.
Application to Geometric Proofs: e.g. proving triangle properties like isosceles, right-angled.
Unit 2: Coordinate Geometry and Introduction to Geometric Proof
2.1 Coordinate Geometry in Problem Solving
Modelling Figures with Coordinates: placing triangles, quadrilaterals, and other shapes in the plane for analysis.
Using Algebra to Justify Geometric Properties: congruence, parallelism, perpendicularity, equal length.
Area of Plane Figures: triangle and polygon area using determinant or formula-based methods.
2.2 Line Segments and Geometric Reasoning
Dividing Line Segments: internal division in a given ratio.
Collinearity and Concurrent Lines: establishing conditions using coordinates.
Use of Coordinate Geometry in Proofs: combining distance, gradient, and midpoint results to verify claims.
2.3 Applications and Modelling Contexts
Applied Geometry: e.g. designing structures with perpendicular supports, checking safety margins with distance constraints.
Interpretation of Geometric Models: understanding and analysing location-based or motion-related scenarios using linear equations.
Units 1 & 2 (Linear and Coordinate Geometry)
Focus on developing algebraic and graphical understanding of linear relationships, interpreting and constructing equations from geometric contexts, and working fluently with gradient, distance, midpoint, and parallel/perpendicular lines in the Cartesian plane. Introduces basic proof techniques using algebra and coordinates.
Unit 1: Linear Relationships and Cartesian Geometry
1.1 Linear Equations and Graphs
Form of Linear Equations: gradient-intercept form (y = mx + c), point-gradient form, general form (Ax + By + C = 0).
Gradient: interpreting as rate of change, calculating from two points.
Graphing Techniques: plotting using intercepts, gradient and point, or technology.
Contextual Applications: e.g. cost/revenue models, constant rate scenarios.
1.2 Parallel and Perpendicular Lines
Parallel Lines: identical gradients; solving geometric problems using this property.
Perpendicular Lines: product of gradients = –1; proving relationships between lines.
Intersecting Lines: solving simultaneous linear equations algebraically and graphically.
1.3 Distance and Midpoint Formulae
Distance: derived from Pythagoras’ Theorem, applied to two points in the plane.
Midpoint: average of coordinates, used in bisector and triangle centre problems.
Application to Geometric Proofs: e.g. proving triangle properties like isosceles, right-angled.
Unit 2: Coordinate Geometry and Introduction to Geometric Proof
2.1 Coordinate Geometry in Problem Solving
Modelling Figures with Coordinates: placing triangles, quadrilaterals, and other shapes in the plane for analysis.
Using Algebra to Justify Geometric Properties: congruence, parallelism, perpendicularity, equal length.
Area of Plane Figures: triangle and polygon area using determinant or formula-based methods.
2.2 Line Segments and Geometric Reasoning
Dividing Line Segments: internal division in a given ratio.
Collinearity and Concurrent Lines: establishing conditions using coordinates.
Use of Coordinate Geometry in Proofs: combining distance, gradient, and midpoint results to verify claims.
2.3 Applications and Modelling Contexts
Applied Geometry: e.g. designing structures with perpendicular supports, checking safety margins with distance constraints.
Interpretation of Geometric Models: understanding and analysing location-based or motion-related scenarios using linear equations.
About Author
Samit believes fitness isn’t just about working out—it’s about taking care of your body. His classes focus on deep stretching, muscle recovery, and stress relief techniques to help students move better and feel their best every day.
Samit believes fitness isn’t just about working out—it’s about taking care of your body. His classes focus on deep stretching, muscle recovery, and stress relief techniques to help students move better and feel their best every day.
Samit believes fitness isn’t just about working out—it’s about taking care of your body. His classes focus on deep stretching, muscle recovery, and stress relief techniques to help students move better and feel their best every day.
