16 Questions
According to the story, what was René Descartes staring at when he realized he could describe its location using perpendicular lines?
A fly crawling on the ceiling
What are the two numbers used to locate an object in a two-dimensional plane?
Displacement from the horizontal axis and the vertical axis
What is the point at which the two axes cross called?
The origin
In which direction do the positive numbers increase on the y-axis?
Upwards
How many sections does the Cartesian coordinate system divide the plane into?
Four
What is the name of the system that René Descartes introduced?
The Cartesian coordinate system
How are the quadrants numbered in the Cartesian coordinate system?
Counterclockwise
What is the label of the lower right section of the Cartesian coordinate system?
Quadrant IV
What is represented by the arrowheads in Figure 3?
The extension of the axes to positive and negative infinity
How is a point in the plane identified?
By its x- and y-coordinates
What is an ordered pair also known as?
A coordinate pair
How is the point (3, -1) represented in the plane?
By moving three units to the right and one unit down from the origin
What is the primary purpose of a rectangular coordinate system?
To show the relationship between two quantities
What is the x-axis?
The horizontal axis
How can the x-axis and y-axis be divided and labeled?
They can be divided and labeled by different increments
What can the axes in a rectangular coordinate system represent?
Other units, such as years or quantity
Study Notes
The Cartesian Coordinate System
- The Cartesian coordinate system is a grid system with perpendicular axes, introduced by René Descartes, a 17th-century philosopher and mathematician.
- The system is based on a two-dimensional plane consisting of a horizontal axis (x-axis) and a vertical axis (y-axis).
- The axes divide the plane into four sections, called quadrants, numbered counterclockwise: I, II, III, and IV.
Axes and Quadrants
- The x-axis is the horizontal axis, and the y-axis is the vertical axis.
- The center of the plane is the origin, or point (0,0), where the two axes cross.
- Each axis is divided into equal units, with increasing positive numbers to the right on the x-axis and up the y-axis, and decreasing negative numbers to the left on the x-axis and down the y-axis.
Ordered Pairs
- Each point in the plane is identified by its x-coordinate (horizontal displacement from the origin) and its y-coordinate (vertical displacement from the origin).
- The x- and y-coordinates are written together as an ordered pair, (x,y), indicating the combined distance from the origin.
- An ordered pair is also known as a coordinate pair, consisting of x- and y-coordinates.
Plotting Points
- A point in the plane can be represented by moving horizontally and vertically from the origin according to its x- and y-coordinates.
- For example, the point (3,−1) can be represented by moving three units to the right of the origin and one unit down.
Explore the concept of plotting ordered pairs in the Cartesian Coordinate System, and learn how it was founded by René Descartes.
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