What are coordinates of points?

This is the first in the series of four activities about the coordinates system. In the first of this series of activity, you will learn about coordinates of points on an x-y plane and how to plot them. Here is a drawing of a GeoGebra window that your teacher explained earlier. You use the Move tool to move points and other objects. You use the Point tool to create points.

Activity 1
Before you do the activities answer the following questions.

  1. How far is point E from the x-axis? from the y-axis?
  2. How far is point D from the x – axis? from the y- axis?
  3. How far is point C from the x- axis? from the y – axis?
  4. Can you describe the location of the other points in relation to their distances from the x and y axes?
You can check your answer to these questions by doing the activities in this GeoGebra window:

A. To show the coordinates of a point, do the following steps:

Click the MOVE tool then right click the point; select object properties then go to show label and choose ‘name and value’

Practice: Show the coordinates of the points A, B, C, D, E, F, G, H

Question: What does the first number in the pair of numbers tell you about the location of the point? What about the second number?

Question: The distance of A from the x axis is 1 unit but why is it the the first coordinates shows -1? What does the negative (-), tell you about the location of A?

B. To plot a point with a specific coordinates, say (4,2) type M=(4,2) in the input bar.

Practice exercise:
Plot the following points using the input bar: P(1,1), Q(1,-1), S(-2,-2), T(3, -3)

C. To plot a point anywhere on the coordinate axes:

Click the point tool [.A] and click on the drawing pad where you want the point located.

Solve this problem: (Don’t forget to click the refresh button first. Delete the points which are not part of your final answer.)

One of the corners of a square with area 9 square units is at (0,0). Locate the other corners of the square. How many such squares are there?

Click here to check if you are correct.

You may want to check out the meaning of the following terms: Cartesian plane, abscissa, ordinate, ordered pair. It helps to know other names for the ideas you learned in this activity.

When you are ready go to Activity 2 – What are the coordinates of points under reflection?