Lesson 11Points on the Coordinate Plane

Learning Goal

Let’s explore and extend the coordinate plane.

Learning Targets

  • I can describe a coordinate plane that has four quadrants.

  • I can plot points with negative coordinates in the coordinate plane.

  • I know what negative numbers in coordinates tell us.

Lesson Terms

  • quadrant

Warm Up: Guess My Line

Problem 1

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

    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.

  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.

Activity 1: The Coordinate Plane

Problem 1

  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:

    open applet in presentation mode

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

  3. Plot a point at . Label it . Plot another point at . Label it .

Print Version

  1. Label each point on the coordinate plane with an ordered pair.

    Four points, A, B, C, and D are graphed in the coordinate plane with the origin labeled “O”. The numbers negative 7 through 7 are indicated on the horizontal axis and the numbers negative 5 through 5 are indicated on the vertical axis. Point A is 3 units to the right and 4 units up from the origin. Point B is 7 units to the left and 2 units down from Point A. Point C is 1 unit to the left and 5 units down from Point B. Point D is 9 units to the right and 1 unit up from Point C.

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

  3. Plot a point at . Label it . Plot another point at . Label it .

Problem 2

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

A coordinate plane showing the names of the four quadrants-I, II, III, and IV starting with x and y positive and rotating counter-clockwise.

  1. In which quadrant is located? ? ?

  2. A point has a positive -coordinate. In which quadrant could it be?

Activity 2: Coordinated Archery

Problem 1

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

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

open applet in presentation mode

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

Print Version

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

A coordinate plane with the origin labeled “O”. The numbers negative 13 through 3 are indicated on the horizontal axis and the numbers negative 9 through 2 are indicated on the vertical axis. A target consisting of five concentric circles is located in the center of the coordinate plane. The midpoint of the circle is negative 4.5 comma negative 4. The largest circle is white with a diameter spanning from negative 9.5 to 0.5. The next inner circle is green with a diameter spanning from negative 8.5 to negative 0.5. The next inner circle is blue with a diameter spanning from negative 7.5 to negative 1.5. The next inner circle is red with a diameter spanning from negative 6.5 to negative 2.5. The innermost circle is yellow with a diameter spanning from negative 5.5 to negative 3.5.

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

Are you ready for more?

Problem 1

Pretend you are stuck in a coordinate plane. You can only take vertical and horizontal steps that are one unit long.

  1. How many ways are there to get from the point to if you will only step down and to the right?

  2. How many ways are there to get from the point to if you can only step up and to the right?

  3. Make up some more problems like this and see what patterns you notice.

Lesson Summary

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

A coordinate plane with points plotted. A (2, 3) B (-4, 1) C (-3.5, -3)

The ordered pair can have negative - and -values. For , the -value of -4 tells us that the point is 4 units to the left of the -axis. The -value of 1 tells us that the point is one unit above the -axis.

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