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Coordinate geometry is explored through examples that illustrate how to locate points using two perpendicular axesβx-axis and y-axis. The importance of two coordinates (x, y) to precisely identify a point in the coordinate plane is emphasized, along with its historical context connected to RenΓ© Descartes.
Coordinate geometry is a branch of mathematics that allows us to determine the position of a point in a plane using two perpendicular lines called axes. These axes, termed the x-axis (horizontal) and y-axis (vertical), intersect at a point called the origin (0, 0). The plane formed by these axes is known as the Cartesian or coordinate plane.
The concepts of coordinate geometry trace back to the work of RenΓ© Descartes, a French mathematician who introduced this system to describe the position of points in a plane, enhancing our ability to visualize mathematical principles.
Coordinate System: A framework for identifying points in a two-dimensional space using two axes.
Quadrants: The four distinct sections of the Cartesian plane defined by the signs of the coordinates.
Origin: The point of intersection of the x-axis and y-axis, represented as (0, 0).
When x is positive and y is too, in Quadrant I, it's good for you!
Imagine a city on a map where each house follows a coordinate grid. The mayor asks you to find the school at (2, 3) by following the x and y paths!
Remember Q I is '+' '+', Q II is '-' '+', Q III is '-' '-', Q IV is '+' '-'.
A point A located at (2, 3) is 2 units from the y-axis and 3 units from the x-axis.
In the Cartesian plane, the triangle formed by the points (0, 0), (3, 4), and (3, 0) can be accurately located and graphed using coordinates.
Term: Coordinate
Definition: A set of values that define the position of a point in a plane typically expressed as (x, y).
A set of values that define the position of a point in a plane typically expressed as (x, y).
Term: Quadrant
Definition: One of the four regions of a Cartesian plane formed by the x-axis and y-axis.
One of the four regions of a Cartesian plane formed by the x-axis and y-axis.
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.