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!
Wow! This video was by far the most helpful I’ve watched on this material. By the time you put the last set of problems on the board I was solving them own my own! Most videos make the material “look” easy to do, with yours I can delete the “look” part!
Michael M (on a CCM YouTube video about the Chain Rule)
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