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Ne’er the Twain Shall Meet

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Ne’er the Twain Shall Meet - PowerPoint PPT Presentation

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Ne’er the Twain Shall Meet

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  1. Ne’er the Twain Shall Meet • Before the end of the European Renaissance, math was cleanly divided into the two separate subjects of geometry and algebra. You didn't use algebraic equations in geometry, and you didn't draw any pictures in algebra. Then, around 1637, a French guy named René Descartes came up with a way to put these two subjects together.

  2. Coordinate Plane Cartesian Plane Rene Descartes

  3. x-axis y-axis

  4. (x,y) Cartesian Plane II I 9 8 7 6 5 4 3 2 1 -1 -2 -3 -4 -5 -6 -7 -8 -9 (–,+) (+,+) (-5,2) (5,2) -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 (-5,-2) (5,-2) (–, –) (+, –) III IV

  5. (x,y) Notes I (+,+) (5,2) II (-,+) (-5,2) • Ordered pair (x,y) • Origin (0,0) • x-axis • Horizontal axis • Negative – left • Positive – right • y-axis • Vertical axis • Negative – down • Positive – up • Quadrant (I,II,III,IV) • I is the top right • All others fit counterclockwise on the graph • Scale – the way to change the numbering on the graph so that points with smaller or larger numbers will fit (5,-2) (+,-) IV (-5,-2) (-,-) III