GED Mathematical Reasoning: Coordinate Plane

In this chapter, I’d like to introduce you to the coordinate plane, which is also sometimes referred to as the xy-plane or the Cartesian coordinate system.

All these names refer to the grid formed by the intersection of two number lines where one of the number lines is oriented horizontally and the other is oriented vertically.

The horizontal number line is called the “x” axis and the vertical number line is called the “y” axis. They intersect at zero and this intersection point is called the “origin.”

Because of their intersection, 4 quadrants are formed. The top right quadrant is called “quadrant one” and from there we go counterclockwise. The top left quadrant is called “quadrant two,” the bottom left quadrant is called the “quadrant three,” and the bottom right quadrant is called “quadrant four.”

This grid gives us a place where we can plot points and, later, graph curves.

coord1

To communicate the placement of a point on the coordinate plane, we use an ordered pair. An ordered pair is a set of two numbers enclosed within parenthesis and separated by a comma. We call it “ordered” because the order matters.

(x, y)

The first value in the pair always represents an “x” value. We usually refer to this value as an ‘x-coordinate’ or ‘x-value.’ The second value represents a “y” value and we usually refer to it as a ‘y-coordinate’ or ‘y-value.’

You can remember this ordering because it’s alphabetical – the “x” value always comes before the “y” value, just like in the alphabet.

The x-coordinate tells us how many units left or right, starting at the origin and with respect to the x-axis. A positive number implies RIGHT. A negative number implies LEFT.

The y-coordinate tells us how many units up or down, starting at the origin and with respect to the y-axis. A positive number implies UP. A negative number implies DOWN.

A point lying on the y-axis has an x-coordinate of ZERO and a point lying on the x-axis has a y-coordinate of ZERO.

 

Example 1

Plot the point: (-2, 5)

 

The x-coordinate in this ordered pair is -2. So we’ll start at the origin and move TWO units to the LEFT (in the negative direction). The y-coordinate is positive 5. So from there, we’ll move UP, 5 units.

 

Example 2

Plot the point: (0, -3)

 

The x-coordinate in this example is 0. So we’ll start at the origin and move ZERO units. The y-coordinate is -3, so from there we’ll move THREE units DOWN, since the 3 is negative.

math 245

 

Example 3

Write the ordered pair for Point A shown on the graph.

graph1

 

Beginning at the origin, point A lies 6 units to the RIGHT with respect to the x-axis. That means the x-coordinate will be positive 6. From there, the point lies directly on the x-axis – there is no veritcal change up or down with respect to the y-axis. That means the y-coordinate is ZERO.

So the ordered pair representing point A is: (6, 0)

 

Example 4

Write the ordered pair for Point B shown on the graph.
graph1

 

Beginning at the origin, point B lies 7 units to the LEFT with respect to the x-axis. That means the x-coordinate will be negative 7.

From there, the point lies 9 units DOWN with respect to the y-axis. That means the y-coordinate is -9.

So the ordered pair representing point B is: (-7, -9)

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