Lesson 11: Points on the Coordinate Plane

Let’s explore and extend the coordinate plane.

11.1: Guess My Line

A coordinate plane with the origin labeled “O”. The numbers 0 through 15 are indicated on the horizontal axis and the numbers 0 through 10 are indicated on the vertical axis.

  1. Choose a horizontal or a vertical line on the grid. Draw 4 points on the line and label each point with its coordinates.

  2. Tell your partner whether your line is horizontal or vertical, and have your partner guess the locations of your points by naming coordinates.

    If a guess is correct, put an X through the point. If your partner guessed a point that is on your line but not the point that you plotted, say, “That point is on my line, but is not one of my points.”

    Take turns guessing each other’s points, 3 guesses per turn. 

11.2: The Coordinate Plane

  1. The colored points on the coordinate plane are like targets. Hit each point by entering its coordinates as an ordered pair in the Input Bar, like this:

    GeoGebra Applet Gv5SZba6

  2. What do you notice about the locations and ordered pairs of $B$, $C$, and $D$? How are they different from those for point $A$?

  3. Plot a point at $(\text-2, 5)$. Label it $E$. Plot another point at $(3, \text-4.5)$. Label it $F$.

  4. The coordinate plane is divided into four quadrants, I, II, III, and IV, as shown here.

    An xy-coordinate plane with the origin labeled "O". The region to the right of the y-axis and above the x-axis is labeled "Quadrant I." The region to the left of the y-axis and above the x-axis is labeled "Quadrant II." The region to the left of the y-axis and below the x-axis is labeled "Quadrant III." The region to the right of the y-axis and below the x-axis is labeled "Quadrant IV."

    $G = (5, 2)$

    $H=(\text-1, \text-5)$

    $I=(7,\text-4)$

    1. In which quadrant is $G$ located? $H$? $I$?
    2. A point has a positive $y$-coordinate. In which quadrant could it be?

11.3: Coordinated Archery

Here is an image of an archery target on a coordinate plane. The scores for landing an arrow in the colored regions are:

Yellow: 10 points     Red: 8 points     Blue: 6 points     Green: 4 points     White: 2 points

Name the coordinates for a possible landing point to score:

1. 6 points       2. 10 points       3. 2 points       4. No points       5. 4 points       6. 8 points

Type the coordinates for each point in a separate line, using parentheses. Like this:  

 

Summary

Just as the number line can be extended to the left to include negative numbers, the $x$- and $y$-axis of a coordinate plane can also be extended to include negative values.

The ordered pair $(x,y)$ can have negative $x$- and $y$-values. For $B = (\text-4,1)$, the $x$-value of -4 tells us that the point is 4 units to the left of the $y$-axis. The $y$-value of 1 tells us that the point is one unit above the $x$-axis. 

The same reasoning applies to the points $A$ and $C$. The $x$- and $y$-coordinates for point $A$ are positive, so $A$ is to the right of the $y$-axis and above the $x$-axis. The $x$- and $y$-coordinates for point $C$ are negative, so $C$ is to the left of the $y$-axis and below the $x$-axis.

Practice Problems ▶

Glossary

quadrant

quadrant

When axes extend in both positive and negative directions, the coordinate plane is divided into 4 regions called quadrants. The quadrants are numbered with Roman numerals, with quadrant I in the upper right, quadrant II in the upper left, quadrant III in the lower left, and quadrant IV in the lower right.