Mathematics for Teaching GeoGebra Activities How to describe sets of points algebraically – Part 1?

How to describe sets of points algebraically – Part 1?

This is the third of the series of 4 worksheets about points and lines on Cartesian Plane

  1. Activity 1 – What is the meaning of coordinates of points?
  2. Activity 2 – What are the coordinates of points under reflection?
  3. Activity 3 – How can we describe sets of points by an equation?

In Activity 1 you learned how to describe the position of points in Cartesian plane in terms of its coordinates. In Activity 2 you learned about the sign of the coordinates in each quadrant in the Cartesian plane. Most importantly you learned to predict the coordinates of points reflected along the x and y axes. In this Activity you will learn how to describe a set of points that belong to a line by an equation. You will also learn how to use the line tool and how to input equations in the input bar.

Activity 3 – How to describe a set of points

In Activity 2 you came up with the following arrangement of points. I changed the colors and size of the points. You will learn how to do this later.

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Part A

  1. What do you notice about the coordinates of the set of green points, that is E’, F’, G’ …E’1?
  2. Use the line tool to draw a line along the points. To do this, click the line tool, then click on any two points in E, F, …K. You can also change the color of the line. To do this right click the line, choose object properties, then choose color.
  3. Go back to the point tool [.A] and click on the line you draw in #2 to draw a point. Show the coordinates of this point to verify your answer in #1. Move the point along the line and observe the changing coordinates. Do the coordinates have the same relationship as the other points on the line?
  4. Optional: Plot a point on the line by typing P=(-3.2,3.5) in the input bar. Show the coordinates of P. Drag P. What do you notice? The point M in #3 is dependent on the line while P is independent of the line.
  5. How are x and the y coordinates of each of the red points related? Can you write this relationship in equation form?

Part B

Follow the instruction and answer the 5 questions in Part A but this time use the red points – E, F, G … .

When you are ready go to Activity 4