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This section explains the Cartesian coordinate system, where points are identified based on their distances from two perpendicular axes. It introduces concepts like coordinates, quadrants, and the significance of the origin, providing a basis for understanding concepts in coordinate geometry.
The Cartesian system is a way of representing points in a two-dimensional space using two perpendicular lines, called the x-axis and y-axis. This section begins with a brief overview of how points can be defined in a linear system and transitions into the more complex idea of a two-dimensional coordinate plane.
The system allows for a clear and precise representation of spatial relationships, making it fundamental for higher mathematical concepts.
Coordinate System: A method for pinpointing the location of a point in a plane using two axes.
Quadrants: The four sections of the Cartesian plane formed by the intersecting axes.
Origin: The (0, 0) point where the x and y axes intersect.
Coordinates: The (x, y) values that specify a point's position relative to the origin.
The origin's point is zero and zero, where all lines meet, that's where we go!
Imagine a treasure map where the x-axis is a horizontal river and the y-axis is a vertical mountain. By using coordinates, you can find treasure by identifying its exact spot.
Remember 'OX is positive and OY is upward' to recall the direction of positive coordinates.
The coordinates of a point located four units to the right and three units up from the origin is (4, 3).
A point at (-2, -5) indicates it is two units left and five units down from the origin.
Term: Cartesian Plane
Definition: A two-dimensional plane defined by a horizontal line (x-axis) and a vertical line (y-axis) intersecting at the origin.
A two-dimensional plane defined by a horizontal line (x-axis) and a vertical line (y-axis) intersecting at the origin.
Term: Coordinates
Definition: A pair of values (x, y) that define the position of a point in the Cartesian plane.
A pair of values (x, y) that define the position of a point in the Cartesian plane.
Term: Origin
Definition: The intersection point of the x-axis and y-axis, represented as (0, 0).
The intersection point of the x-axis and y-axis, represented as (0, 0).
Term: Quadrants
Definition: The four sections of the Cartesian plane created by the axes.
The four sections of the Cartesian plane created by the axes.
Term: Abscissa
Definition: The x-coordinate of a point in the Cartesian plane.
The x-coordinate of a point in the Cartesian plane.
Term: Ordinate
Definition: The y-coordinate of a point in the Cartesian plane.
The y-coordinate of a point in the Cartesian plane.