AC9M9A03

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

AC9M9A03_E1 - 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
AC9M9A03_E2 - 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 (-\(1\))
AC9M9A03_E3 - using Pythagoras’ theorem to establish the distance between \(2\) points in the Cartesian plane and applying this using horizontal and vertical distances and coordinates
AC9M9A03_E4 - investigating graphical and algebraic techniques for finding the midpoint and gradient of the line segment between \(2\) points
AC9M9A03_E5 - 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

Achievement Standard Components

ASMAT904 - They find the distance between 2 points on the Cartesian plane, and the gradient and midpoint of a line segment.