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Math Analytic Geometry

This is where algebra, geometry, and trigonometry meet. In other words, this is classical analytic geometry (necessary because analytic geometry has also a more modern meaning).

In short, common language it is about graphing, the basics of which are introduced in elementary school with "number lines." Two dimensional and three dimensional graphs are usually introduced in high school algebra and are used in most approaches to trigonometry. Thus, most of the concepts are familiar to students of analytic geometry, so it is often a short course or is combined with other material in a "pre-calculus" course.

Analytic geometry accepts both algebraic and geometric arguments, providing students who remember their geometry with a chance to shine. Often a one-page geometry proof is the equal of five pages of algebra.

Number as Length

The association of number and length must be very old historically. For students it is old too. The number line is introduced very early, although it may be only the non-negative part at first. The arrow heads obviously do not indicate the positive direction, but are a pedagogic device to reinforce the idea that the lines could be extended indefinitely in either direction.

Number Line -5 -4 -3 -2 -1 0 1 2 3 4 5 Number Line

Grid Number Line X-Axis -5 -4 -3 -2 -1 1 2 3 4 5 Number Line Y-Axis -5 -4 -3 -2 -1 1 2 3 4 5 O x y Rectangular Co-ordinate Plane

Point-Slope Formula

{$$ y - y_1 = m(x - x_1) $$}

L O 1 2 3 4 5 6 30° 60° 120° 150° 210° 240° 300° 330° 90° 270° 180°
Polar Co-Ordinate Plane


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This is a student's notebook. I am not responsible if you copy it for homework, and it turns out to be wrong.

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August 05, 2017

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