This course introduces coordinate geometry, where every point in a plane is described by a pair of numbers. You learn the axes, the origin, the four quadrants and how to plot and reflect points. Then you derive the distance formula from Pythagoras' theorem and use it to test triangles and collinear points. The section formula and the midpoint formula locate points dividing a segment in a given ratio. You find the centroid of a triangle and its area straight from the coordinates of its vertices, and finally combine these tools to identify parallelograms, rectangles, rhombuses and squares and to find a point equidistant from three others.
Middle Years
Introduction to Coordinate Geometry
Points as pairs of numbers: the Cartesian plane, the distance formula, the section and midpoint formulas, the centroid and area of a triangle, and testing quadrilaterals with coordinates.
- 5 lessons
Overview
Lessons
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The Cartesian plane
The x-axis, y-axis and origin, coordinates of a point, the signs in the four quadrants, points on the axes, reflections, and simple shapes on the grid.
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The distance formula
Deriving the distance between two points from Pythagoras' theorem, and using it to test triangles, check collinear points and find unknown coordinates.
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The section formula and the midpoint
The point dividing a segment in the ratio m : n, the midpoint formula, finding a missing endpoint, finding the ratio of division, and points of trisection.
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Centroid and area of a triangle
The centroid as the average of the vertices, the area of a triangle from its coordinates, the zero-area test for collinear points, and areas of quadrilaterals.
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Quadrilaterals with coordinates
Deciding whether four points form a parallelogram, rectangle, rhombus or square, finding a missing vertex, and the point equidistant from three points.