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What Are The Different Parts of a Graph Plotting Points on The Coordinate Plane End Point Definition Formula Math Coordinates Definition Concept Undefined Slope Definition Examples Vertical Line Equation Slope

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GMAT: What is a Number Line
Math Coordinates Definition Concept

In this lesson, we will learn about Cartesian math coordinates. Math coordinates give a location on a map or graph. The math coordinates are a way to locate the point on a graph or map, like an address.

Math Coordinates Definition Concept

What are Math Coordinates?

Math coordinates are a way to show an address to a point on a Cartesian coordinate system. We can interchange these two terms, math coordinates and Cartesian coordinates, because they are the same thing. This system is a tool used to graph points, lines and curves.

Math coordinates can also be called ordered pairs. The ordered pair, written like this (x,y), give a location on a map or graph that is indicated by up/down or left/right directions. This allows us to precisely locate a point.

Cartesian Coordinate System: How to set it up

When looking at a graph, the vertical number line is called the y-axis. The horizontal line is called the x-axis.

Cartesian Coordinate System

Notice the two number lines cross each other at the point (0,0). This is called the origin. The origin is where you begin. Right is positive and left is negative on the x-axis. Up is positive and down is negative on the y-axis.

Ordered Pairs: Location, Location, Location

The Cartesian coordinate system is divided into four areas. The top right segment is called quadrant I. Then moving counter-clockwise, we have quadrant II, then quadrant III, then quadrant IV.

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As you work through the four quadrants, you can see the ordered pairs have a very specific value for each quadrant:

Quadrant I - x-coordinate will be positive and the y-coordinate will be positive, (x,y)
Quadrant II - x-coordinate will be negative and the y-coordinate will be positive, (-x, y)
Quadrant III - x-coordinate will be negative and the y-coordinate will be negative, (-x, -y)
Quadrant IV - x-coordinate will be positive and the y-coordinate will be negative, (x, -y)

Understanding this will help you to graph each point quickly. For instance, if you were given, (-3, -9), you know the point will be in the third quadrant. If given, (4, -5), you know it will be in the fourth quadrant.

Examples of math coordinates

The ordered pair, (2,5), is the address of point A. The first value, 2, says to move from the origin two steps to the right since 2 is a positive number. From here, we move 5 steps up. Since 5 is positive, we want to move in a positive direction. If you notice, we moved right 2, then up 5 steps.

Let's use the ordered pair (-1, -9) to plot point B. Using -1 as our x-value, we move 1 step to the left of the origin, then 9 steps down from there. We moved 1 left, then down 9.

Let's graph a few points:

Graph point X at (-2, 5) or 2 steps left, 5 steps up.
Graph point Y at (5,-2) or 5 steps right, 2 steps down.
Graph point P at (-7, -6) or 7 steps left, 6 steps down.
Graph pointR at (8, 3) or 8 steps right, 3 steps up.

X-intercepts and Y-intercepts: Points on the Axis

Plot point C (0, 6) and plot point D (-4, 0)

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These points are called x-intercepts and y-intercepts. Point C sits on the y-axis and is called the y-intercept since it 'intercepts the y-axis'. Point D sits on the x-axis and is called the x-intercept. Notice each of the math coordinates have a zero in the address. If the zero is the x-coordinate, it is a y-intercept, (0,y). If the zero is the y-coordinate, it is the x-intercept (x,0).