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In this introductory section, students learn the importance of describing the positions of points on a plane relative to two reference lines, which can be horizontal and vertical. Key examples illustrate how coordinates facilitate precise location identification, leading to the development of coordinate geometry.
In the study of coordinate geometry, points are located in a plane using two perpendicular reference lines. The section begins by reviewing the previous knowledge of the number line and the need to define positions in two dimensions. The examples include locating houses on intersecting streets and determining the position of a dot on paper using measurements from two fixed lines. An interactive classroom activity involving creating a seating plan reinforces the concept that two independent pieces of information are required to describe the position of an object. This introduction establishes the significance of this geometric approach and its historical context, notably through the contributions of René Descartes, whose Cartesian coordinate system forms the underlying structure of this branch of mathematics.
Cartesian Coordinate System: A system for describing points in a plane using two perpendicular lines.
Coordinates: The values that represent a point's position, typically written as (x, y).
Abscissa and Ordinate: The x-coordinate and y-coordinate of a point, respectively.
Quadrants: The four sections created by the intersection of the x-axis and y-axis.
In a Cartesian plane, two lines will reign, one goes across, the other, up, it's plain!
Once in a land of graphs, two lines crossed at a point, and all the houses in the neighborhood lived happily at their coordinates.
Remember: ‘X is the first, Y is the next; in coordinates, that’s how we connect!’
To find the location of a house at (5, 3), you would first locate Street 5 and then find House 3 on that street.
When plotting a point like (4, -2), move 4 units to the right on the x-axis and 2 units down on the y-axis.
Term: Coordinate
Definition: A set of values that show an exact position in a two-dimensional space, typically represented as (x, y).
A set of values that show an exact position in a two-dimensional space, typically represented as (x, y).
Term: Cartesian System
Definition: A coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates.
A coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates.
Term: Abscissa
Definition: The x-coordinate of a point in a Cartesian system.
The x-coordinate of a point in a Cartesian system.
Term: Ordinate
Definition: The y-coordinate of a point in a Cartesian system.
The y-coordinate of a point in a Cartesian system.
Term: Quadrant
Definition: One of the four sections of a Cartesian plane divided by the x-axis and y-axis.
One of the four sections of a Cartesian plane divided by the x-axis and y-axis.