A coordinate grid works by using numbers to precisely locate points on a flat surface. Think of it like a map where you use a system of coordinates to find specific locations.
The Basics of Locating Points
At its core, a coordinate grid provides a structured way to describe where any point is situated. As the reference states, "The numbers on a coordinate grid are used to locate points." This is achieved through a system based on two perpendicular lines, typically called the x-axis (horizontal) and the y-axis (vertical).
Using Ordered Pairs (x, y)
Every single point on the grid can be uniquely identified. "Each point can be identified by an ordered pair of numbers," according to the reference. This pair is always written in a specific order, inside parentheses, like this: (x-coordinate, y-coordinate).
- The first number in the pair is the x-coordinate. This number tells you how far to move along the x-axis (horizontally).
- The second number is the y-coordinate. This number tells you how far to move along the y-axis (vertically).
The reference clearly defines these: "that is, a number on the x-axis called an x-coordinate, and a number on the y-axis called a y-coordinate." And it specifies the format: "Ordered pairs are written in parentheses (x-coordinate, y-coordinate)."
Plotting a Point
To find or "plot" a point on the grid using its ordered pair:
- Start at the origin (the point where the x and y axes intersect, which is the point (0,0)).
- Move right or left along the x-axis according to the x-coordinate. (Right for positive numbers, left for negative numbers).
- From that position on the x-axis, move up or down parallel to the y-axis according to the y-coordinate. (Up for positive numbers, down for negative numbers).
- The spot where you stop is the location of the point.
Examples
Let's look at a few examples:
- (3, 2): Move 3 units right from the origin, then 2 units up.
- (-1, 4): Move 1 unit left from the origin, then 4 units up.
- (0, -5): Stay at the origin on the x-axis, then move 5 units down.
Using ordered pairs allows us to describe the exact position of any point on the grid, making it an essential tool in mathematics, graphing, and many other fields.
