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 attend university in the US and am starting the more difficult math courses. I have never studied and managed to stumble along for a very long time and now I have no idea what I am doing. I can follow along with lecture and understand what they are saying but when left on my own I have no clue what to do and where to start. So I’ve recommitted to start over and build a solid foundation. Looking around youtube alot I have found some good quick fix stuff but man I am converted to Graeme Hendersen. I really appreciate your very thorough approach to learning and can’t get enough of your explaining mathematical concepts. I am eating up everything and am excited to master math. Man, I sound super nerdy but it’s true. Thanks
Garett M (on a CCM YouTube video about How to Find the Equation of a Parallel Line in 4-5 Lines of Work)
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