The great revolution that René Descartes (1596-1650) started allowed mathematicians to convert geometric problems into algebraic ones by placing shapes and construction lines on grid paper. In order to achieve this, they learned techniques for setting up equations for lines and curves, and ways of calculating significant details about graphs (points, lengths, angles, areas, etc.) using algebra.
The relationship between geometry and algebra even worked in reverse. Using algebraic arguments, mathematicians were able to prove that some classic problems in geometry actually impossible to solve.
Your journey with coordinate geometry begins with learning to locate points, then the midpoints between them, and then equations for lines, gradients of lines, lengths of intervals, etc. In time, you will also learn to divide intervals into particular ratios, to calculate angles between lines, and to calculate the distance from a point to a line.
You will then learn how to construct equations for lines and curves from geometric principles (viewing them as loci).
All these skills will enhance your ability to solve difficult geometric problems using the power of algebra.
A huge adventure awaits you!
Our boys received a distance education and required additional tuition in their higher level of Maths. Graeme undertook this for us which brought together both his professional expertise and the motivation required for our boys to achieve the excellent results that we all hoped for. Today our boys are following their chosen career paths and we will always remain grateful for Graeme’s part in that. We warmly commend Graeme’s tuition and dedication to his students to you.
David and Mary T (parents, c2006-2012)
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