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!
I would describe Graeme as one of the best tutors I ever had. During my school years I spent some time attending one of the major tutoring organizations in town and I found it was difficult for the tutors to spend the time needed to assist me with problem solving due to the class size. My mother rang a private tutor in the phone book who gave her Graeme’s phone number as he specialized in tutoring high school students and was a teacher who used to work at my school. He offered a tutoring service at convenient times which suited our busy life style. The one-on-one service that Graeme provides was what I needed and I saw improvements straight away with my exam results. This made my parents very happy and I found a new confidence in approaching exams. I have since left school but have stayed in contact with Graeme and he has provided me with terrific practical suggestions in preparing for interviews. I would not hesitate in recommending Graeme as a great teacher.
James C (Student, 2012)
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