Geometry and Measurement: Position and orientation, Level 6
AO1: Use a co-ordinate plane or map to show points in common and areas contained by two or more loci.
This means the students will be able to use algebra and graphing to find a point in common with two intersecting lines when given their equations and connect this understanding with contexts that can be modelled with simultaneous linear equations in two variables. A loci is a set of points satisfying a given condition so common examples are lines, circles and ellipses, parabolas, and hyperbolas.
They should be able to sketch the locus for a given condition and recognise when that condition meets that of a conic section, e.g. perimeter of the flight area of a jet taking off and returning to a moving aircraft carrier (ellipse). Using graphing techniques students should be able to find the point or points in common between a line (given two points) and a conic (given the condition) and describe the area bounded by common lines and conics, for example, the grazing area of a tethered animal constrained by a wall.
