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!
You, sir, are the best teacher I’ve ever known in my life. You made maths the most interesting subject for me. I really can’t express my gratitude in words for your amazing teaching!! I never knew integration could be so easy! You are the reason why I excel at all my tests.
Thank you very much for these videos sir …
Sahil D (on a CCM YouTube video explaining How to Integrate With Speed ~ Recognise and Use ‘Integration by Parts’ Pattern )
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