Square sides

Square sides

Work with a partner to construct a square and investigate a directly proportional relationship.

These are the GeoGebra tools you will use in this task:

GeoGebra Slider tool

Slider tool

GeoGebra Move tool

Move tool

GeoGebra New Point tool

New Point tool

GeoGebra Polygon tool

Polygon tool

GeoGebra Perpendicular Line tool

Perpendicular Line tool

  1. Open GeoGebra.
    Download GeoGebra or access the applet online from the Geogebra or download page at https://www.geogebra.org/download .

  2. Create a slider:

    1. Click on the Slider tool.

    2. Click on the grid (perhaps near the top left corner of the grid).

    3. A window appears.

      1. Type ‘a’ for the name.

      2. Set the ‘min’ value to zero.

      3. Set the ‘max’ value to 5.

      4. Set the increment to 1.

      5. Click OK.

  3. Leave the slider on the value of 1 (it should say ‘a = 1’).

  4. In the input box at the top left of the screen, type 'A = (a,a)' and press Enter. Point A appears at (1,1). This point will be a vertex of the square.

  5. The next vertex will be on the x-axis.

    1. Click on the Perpendicular Line tool.

    2. Click on point A.

    3. Click on the x-axis. A vertical line appears through A

    4. Using the New Point tool, click on the point where this vertical line meets the x-axis i.e. (1,0).

  6. The next vertex will be the origin. Click on (0,0)

  7. The final vertex will be on the y-axis.

    1. Click on the Perpendicular Line tool.

    2. Click on point A.

    3. Click on the y-axis. A horizontal line appears

    4. Using the New Point tool, click on the point where this horizontal line meets the y-axis i.e. (0,1).

  8. To draw the square, change to the Polygon tool, and click on points A, B, C, D and then point A again.

  9. Change to the Move tool and slide the slider. The size of the square should change.

  10. Complete this table of values:
    5 column table: label in first cell of top row is 'Perimeter'; second row label is 'Side Length' followed by values 1, 2, 3, 4 in remaining cells.

  11. What is the constant of proportionality between the perimeter and the side length?

  12. Type ‘A = (2a,a)’ into the input box and press Enter. Slide the slider.

    1. What is the constant of proportionality between the y-coordinate of A and the x-coordinate of A?

      (Hint: If you are not sure of the answer, draw up a table of values, slide the slider and record the coordinates in your table.)

  13. What is the constant of proportionality between the perimeter and the smaller side length of the rectangle?

  14. Challenge: Can you type in new coordinates of A so that the constant of proportionality between the perimeter and the smaller side length of the rectangle is 5?