Linear relationships C (Path)
Mathematics K–10 (2022) · Stage 5 · View this focus area on the NESA NSW Curriculum website ↗
Outcomes
MA5-LIN-P-01 describes and applies transformations, the midpoint, gradient/slope and distance formulas, and equations of lines to solve problems (Path: Adv)Content dot points
Each dot point has its own page with resources matched to it.
Apply formulas to find the midpoint and gradient/slope of an interval on the Cartesian plane
- Apply the formula to find the midpoint of the interval joining 2 points on the Cartesian plane: M(x,y) = ((x_1 + x_2)/2,(y_1 + y_2)/2) 4 resources · 1 interactive/game
- Use the relationship m = (rise)/(run) to establish the formula for the gradient/slope (m) of the interval joining the 2 points (x_1,y_1) and (x_2,y_2) on the Cartesian plane: m = (y_2 - y_1)/(x_2 - x_1)
- Apply the gradient formula to find the gradient of the interval joining 2 points on the Cartesian plane 4 resources · 1 interactive/game
Apply the distance formula to find the distance between 2 points located on the Cartesian plane
- Apply knowledge of Pythagoras’ theorem to establish the formula for the distance (d) between the 2 points (x_1,y_1) and (x_2,y_2) on the Cartesian plane: d = √((x_2 - x_1)² + (y_2 - y_1)²) 1 resource · 1 interactive/game
- Apply the distance formula to find the distance between 2 points on the Cartesian plane 4 resources · 1 interactive/game
Use various forms of the equation of a straight line
- Rearrange linear equations from gradient–intercept form (y = mx + c) to general form (ax + by + c = 0) and vice versa
- Find the x- and y-intercepts of a straight line in any form
- Graph the equation of a straight line in any form 5 resources · 4 interactive/game
- Use the point–gradient form (y - y_1 = m(x - x_1)) or the gradient–intercept form (y = mx + c) to find the equation of a line passing through a point (x_1,y_1), with a given gradient m 2 resources · 2 interactive/game
- Use the gradient and the point–gradient form to find the equation of a line passing through 2 points 3 resources · 1 interactive/game
- Find the equation of a line that is parallel or perpendicular to a given line in any form 2 resources
- Determine and justify whether 2 given lines are parallel or perpendicular 2 resources · 1 interactive/game
Solve problems by applying coordinate geometry formulas
Identify line and rotational symmetries
- Identify lines (axes) and rotational symmetry in plane shapes 6 resources · 2 interactive/game
- Identify line and rotational symmetry in various linear and non-linear graphs 1 resource · 1 interactive/game
Describe translations, reflections in an axis, and rotations through multiples of 90 degrees on the Cartesian plane, using coordinates
- Apply the notation P' to name the image resulting from applying a transformation to a point P on the Cartesian plane
- Determine and plot the coordinates for P' resulting from translating P one or more times 5 resources · 1 interactive/game
- Determine and plot the coordinates for P' resulting from reflecting P in either the x - or y -axis 6 resources · 1 interactive/game
- Determine and plot the coordinates for P' resulting from rotating P by a multiple of 90^° about the origin 6 resources · 1 interactive/game
Focus area resources
- Unit/PlanningStage 5 Unit 2 – working with triangles (sample unit of learning)
- Unit/PlanningStage 5 Unit 6 – constant rates of change (sample unit of learning)
Stage 5 planning resources
Stage- or course-wide documents (scope and sequences, guides) that cover this focus area alongside others.
- Unit/PlanningSample scope and sequence: Stage 5 core and selected paths (NESA no. 03)
- Unit/PlanningSample scope and sequence: Stages 4–5 core and selected paths (NESA no. 04)
- Unit/PlanningSample scope and sequence: Stage 5 core and all paths (NESA no. 05)
- Unit/PlanningSample scope and sequence: Stage 5 core (NESA no. 02)
- Unit/PlanningSample scope and sequence: Stage 5 core and selected paths (NESA no. 06)
- Unit/PlanningSample scope and sequence: Stage 5 core and selected paths (NESA no. 01)
- Unit/PlanningSample scope and sequence: Stages 4–5 stage based (NESA no. 08)
- Unit/PlanningStage 5 – sample scope and sequence
- Unit/PlanningStage 5 – stage based – sample scope and sequence