AC9M9A03 Year 9 Mathematics

Content descriptor find the gradient of a line segment, the midpoint of the line interval and the distance between 2 distinct points on the Cartesian plane

Elaborations

• • Elaboration recognising that the gradient of a line is calculated using the gradient of a line segment on that line and is independent of which 2 distinct points on the line are used for this calculation
• • Elaboration using digital tools and transformations to illustrate that parallel lines in the Cartesian plane have the same gradient and that the relationship between the gradients of pairs of perpendicular lines is that their product is (-1)
• • Elaboration using Pythagoras’ theorem to establish the distance between 2 points in the Cartesian plane and applying this using horizontal and vertical distances and coordinates
• • Elaboration investigating graphical and algebraic techniques for finding the midpoint and gradient of the line segment between 2 points
• • Elaboration using dynamic graphing software and superimposed images; for example, playground equipment, ramps and escalators, to investigate gradients in context and their relationship to rule of a linear function, and interpret gradient as a constant rate of change in linear modelling contexts
• • Elaboration investigating how coordinate geometry and aspects of linear algebra play a fundamental role in machine learning and predictive algorithms; for example, object detection and navigation by autonomous vehicles