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In this section, we explore the Cartesian coordinate plane, characterized by its horizontal x-axis and vertical y-axis. Special points like the origin and the significance of quadrants are discussed, along with the definitions of x-coordinates and y-coordinates.
In this section, we delve into the essential aspects of the Cartesian coordinate system. The coordinate system consists of two perpendicular lines—referred to as the x-axis (horizontal) and the y-axis (vertical)—which intersect at a point called the origin (0,0). The introduction of these axes divides the coordinate plane into four distinct regions known as quadrants, each characterized by a unique combination of positive and negative coordinates for x and y. The x-coordinate (or abscissa) indicates a point's horizontal distance from the y-axis, while the y-coordinate (or ordinate) represents the vertical distance from the x-axis. Overall, an understanding of coordinates is vital for locating points on the Cartesian plane, as points are represented in the form (x, y), with various conditions applying for points lying on the axes. Additionally, the convention for coordinates in different quadrants is established, underscoring the relationship between the signs of x and y values.
Cartesian Coordinate System: A system that uses two axes to define a point in a plane.
Origin: The intersection point of the x-axis and y-axis at (0,0).
Quadrants: Four sections of the Cartesian plane, each with distinct signs for x and y coordinates.
Coordinates: Represented as (x, y), where x is the distance from the y-axis and y is the distance from the x-axis.
In Quadrant I where the sun shines bright, both x and y are positive—what a sight!
Imagine a treasure map on a grid. The treasure's coordinates tell you to go 4 steps east (right) and 3 steps north (up) from the origin to find gold!
Use ‘Naughty Students Playing Angry’ to remember: In quadrant I (+,+), II (-,+), III (-,-), and IV (+,-).
Point (5, 3) is located 5 units to the right and 3 units up from the origin.
Point (-2, 7) is located 2 units to the left and 7 units up from the origin.
Term: Cartesian Coordinate System
Definition: A two-dimensional coordinate system defined by two perpendicular axes, the x-axis and y-axis.
A two-dimensional coordinate system defined by two perpendicular axes, the x-axis and y-axis.
Term: Origin
Definition: The point where the x-axis and y-axis intersect, represented as (0,0).
The point where the x-axis and y-axis intersect, represented as (0,0).
Term: Abscissa
Definition: The x-coordinate of a point in the coordinate plane.
The x-coordinate of a point in the coordinate plane.
Term: Ordinate
Definition: The y-coordinate of a point in the coordinate plane.
The y-coordinate of a point in the coordinate plane.
Term: Quadrants
Definition: The four parts of the Cartesian plane formed by the x-axis and y-axis.
The four parts of the Cartesian plane formed by the x-axis and y-axis.