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| title | TARGET DECK | FILE TAGS | tags | |
|---|---|---|---|---|
| Cartesian Coordinate System | Obsidian::STEM | geometry::coordinates |
|
Overview
In plane analytic geometry, the Cartesian coordinate system uniquely specifies a point by a pair of real numbers called its coordinates. These coordinates represent signed distances to the point from two fixed perpendicular oriented lines called the axes. The point where the axes meet is called the origin and have coordinates \langle 0, 0 \rangle.
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Cloze
The {x-coordinate} of a point is sometimes called its {abscissa}.
Reference: Tom M. Apostol, Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra, 2nd ed. (New York: Wiley, 1980).
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Cloze
The {y-coordinate} of a point is sometimes called its {ordinate}.
Reference: Tom M. Apostol, Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra, 2nd ed. (New York: Wiley, 1980).
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Basic
What is an ordinate set?
Back: A set bounded by the x-axis and the graph of a nonnegative function.
Reference: Tom M. Apostol, Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra, 2nd ed. (New York: Wiley, 1980).
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Basic
An ordinate set is bounded below by what?
Back: The x-axis, i.e. y = 0.
Reference: Tom M. Apostol, Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra, 2nd ed. (New York: Wiley, 1980).
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%%ANKI Basic An ordinate set is bounded above by what? Back: The graph of a nonnegative function. Reference: Tom M. Apostol, Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra, 2nd ed. (New York: Wiley, 1980).
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Cloze
The {origin} of a Cartesian coordinate system has coordinates \langle 0, 0 \rangle.
Reference: “Cartesian Coordinate System,” in Wikipedia, October 21, 2024, https://en.wikipedia.org/w/index.php?title=Cartesian_coordinate_system.
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Basic
Consider point \langle x, y \rangle. When does this point lie in the first quadrant?
Back: When x > 0 and y > 0.
Reference: Tom M. Apostol, Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra, 2nd ed. (New York: Wiley, 1980).
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Basic
Consider point \langle x, y \rangle. When does this point lie in the second quadrant?
Back: When x < 0 and y > 0.
Reference: Tom M. Apostol, Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra, 2nd ed. (New York: Wiley, 1980).
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Basic
Consider point \langle x, y \rangle. When does this point lie in the fourth quadrant?
Back: When x > 0 and y < 0.
Reference: Tom M. Apostol, Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra, 2nd ed. (New York: Wiley, 1980).
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Basic
Consider point \langle x, y \rangle. When does this point lie in the third quadrant?
Back: When x < 0 and y < 0.
Reference: Tom M. Apostol, Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra, 2nd ed. (New York: Wiley, 1980).
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%%ANKI Basic The "vertical line test" of a Cartesian coordinate system is used to determine what? Back: Whether the tested graph depicts a function or not. Reference: Tom M. Apostol, Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra, 2nd ed. (New York: Wiley, 1980).
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%%ANKI Basic In Cartesian coordinate systems, why does the vertical line test work? Back: A function is single-valued. A vertical line that intersects a graph multiple times immediately contradicts this. Reference: Tom M. Apostol, Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra, 2nd ed. (New York: Wiley, 1980).
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Cartesian Equations
An equation that completely characters a figure within the Cartesian coordinate system is called a Cartesian equation.
%%ANKI Basic What is a Cartesian equation? Back: An equation that completely characterizes a figure within the Cartesian coordinate system. Reference: Tom M. Apostol, Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra, 2nd ed. (New York: Wiley, 1980).
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Basic
What is the Cartesian equation of a circle centered around the origin with radius r?
Back: x^2 + y^2 = r^2
Reference: Tom M. Apostol, Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra, 2nd ed. (New York: Wiley, 1980).
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Basic
What figure does the following Cartesian equation characterize? x^2 + y^2 = r^2
Back: A circle with radius r centered around the origin.
Reference: Tom M. Apostol, Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra, 2nd ed. (New York: Wiley, 1980).
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Bibliography
- “Cartesian Coordinate System,” in Wikipedia, October 21, 2024, https://en.wikipedia.org/w/index.php?title=Cartesian_coordinate_system.
- Tom M. Apostol, Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra, 2nd ed. (New York: Wiley, 1980).