Precalc0011to0016-page16 - The Cartesian (or rectangular)...

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(Section 0.13: The Cartesian Plane and Circles) 0.13.1 SECTION 0.13: THE CARTESIAN PLANE and CIRCLES LEARNING OBJECTIVES • Understand the Cartesian plane and associated terminology. • Know how to plot points and graph equations in the Cartesian plane. • Know the Distance and Midpoint Formulas. • Be able to recognize, write, standardize, and graph equations of circles. PART A: DISCUSSION • We typically graph an equation in x and y in the Cartesian (or rectangular) plane , named after René Descartes. We plot points using their Cartesian coordinates . • There are alternate coordinate systems. We will discuss polar coordinates in Chapter 6. In three dimensions, we use Cartesian, cylindrical, and spherical coordinates. PART B: THE CARTESIAN (OR RECTANGULAR) PLANE
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Unformatted text preview: The Cartesian (or rectangular) plane is a plane with the Cartesian coordinate system imposed on it. We usually graph in the Cartesian xy-plane , though other variables could be used. We locate a horizontal line called the x-axis and a vertical line called the y-axis . These coordinate axes are real number lines ; at least one nonzero tick mark should be placed on each axis to indicate scale. The axes intersect at the origin , O . A point in the plane corresponds to an ordered pair of the form x-coordinate, y-coordinate ( ) . For example, the origin O corresponds to the ordered pair 0, 0 ( ) , and the red point below corresponds to 2, 3 ( ) . If we name the red point P , we can write P 2, 3 ( ) ....
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