Two numbers are enough to say exactly where a point is on a plane. This course sets up the axes and quadrants and practises plotting, reading and describing positions.
The course follows the Ganita Manjari chapter Orienting Yourself: The Use of Coordinates and has 3 lessons. Each lesson explains the ideas with worked examples and ends with practice questions and full answers. The numbers in every example and question are our own, so the lessons can be used alongside the textbook exercises.
- The Cartesian Plane: Axes, Coordinates and Quadrants, Two perpendicular number lines turn any position in a plane into an ordered pair. The origin, signed distances, points on the axes, the four quadrants and their sign patterns, and reading a floor plan drawn on a grid.
- Distance Between Two Points, Horizontal and vertical segments by subtraction, then the distance formula from the Baudhāyana–Pythagoras theorem; why signs never matter; testing triangles for isosceles, right-angled and collinear; points on a circle; and the midpoint formula.
- Coordinates: Mixed Practice, Twelve questions across the chapter, quadrants and mirror images, distances and perimeters, an equilateral triangle, collinearity, an equidistant point on an axis, midpoints, recovering vertices from midpoints, and icons on a pixel screen.
By the end you will be able to:
- Name the axes, origin and quadrants of the coordinate plane.
- Plot points and read the coordinates of plotted points.
- Find distances between points on the same horizontal or vertical line.
- Describe shapes and paths using coordinates.