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 son Joshua is currently in year 11 preparing for the HSC. Josh was doing reasonably well in mathematics and yet we felt, and his teachers agreed, that if he really applied himself he could be achieving much better results. We asked around for a maths tutor and Graeme Henderson came highly recommended. Joshua began to see Mr Henderson one hour per week and from the very first week Joshua’s motivation escalated. His maths improved to the point where he is now often achieving 100% in his exams, he applies himself to do hours of homework, something he had rarely done in the past, but most of all Josh has found a love of mathematics. Maths is no longer a chore. I believe this all stems from Mr Henderson’s gifted ability not only as a teacher, also as an encourager and motivator. I get motivated just listening to them! Josh told us this week that he wishes he could be tutored every day after school. When the results come through from Joshua’s exams, he is delighted and this has inspired him to become motivated to spend much more time applying himself to his other subjects. Josh is working hard to gain a great result in his HSC. I can personally recommend Mr Henderson as a truly wonderful tutor.
Deborah B (Parent, 2012)
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