91Ó°ÊÓ

The rectangular coordinate system is a two-dimensional plane made by the intersection of two perpendicular lines, called axes. These axes are typically labeled as the x-axis (horizontal) and the y-axis (vertical). Together, they create a grid where every point can be specified by a unique pair of numbers.

The origin is the point where both the x and y axes meet, and it has coordinates \(0,0\). Every other point on the plane is described according to its distance from the origin, in terms of the x (horizontal) and y (vertical) axes. The system divides the plane into four quadrants, where the sign of the x and y coordinates determines in which quadrant a point lies. For instance, in the first quadrant, both x and y are positive, while in the second quadrant, x is negative, and y is positive.

An ordered pair consists of two numbers written in a specific order within parentheses, such as \( x, y \). It is essential to maintain this order because the first number refers to the horizontal position (x-coordinate) and the second to the vertical position (y-coordinate) on the rectangular coordinate system.

Ordered pairs are like addresses for points on a plane. Just as your home has a specific location defined by an address, every point in the coordinate system is represented by its unique ordered pair. A prime example is \( -2, 3 \) from the exercise, where -2 directs you left or right along the x-axis, and 3 guides you up or down the y-axis, thus pinpointing the exact location on the grid.

The x and y coordinates are the two numbers that define an ordered pair in the coordinate system. The x-coordinate, often referred to as the 'abscissa', dictates how far to move horizontally from the origin. A positive x-coordinate means you move to the right, while a negative x-coordinate indicates a move to the left.

Similarly, the y-coordinate, known as the 'ordinate', indicates the vertical displacement from the origin. A positive y-coordinate means moving upwards, and a negative y-coordinate directs you downwards. For the point \( -2, 3 \), the x-coordinate is -2, so you begin at the origin and move 2 units left. The y-coordinate is 3, so from your new position, you move 3 units up. This process places you at the exact location of the point on the grid.