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:
|
|
|
|
|
-
Open GeoGebra.
Download GeoGebra or access the applet online from the Geogebra or download page at https://www.geogebra.org/download . -
Create a slider:
-
Click on the Slider tool.
-
Click on the grid (perhaps near the top left corner of the grid).
-
A window appears.
-
Type ‘a’ for the name.
-
Set the ‘min’ value to zero.
-
Set the ‘max’ value to 5.
-
Set the increment to 1.
-
Click OK.
-
-
-
Leave the slider on the value of 1 (it should say ‘a = 1’).
-
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.
-
The next vertex will be on the x-axis.
-
Click on the Perpendicular Line tool.
-
Click on point A.
-
Click on the x-axis. A vertical line appears through A
-
Using the New Point tool, click on the point where this vertical line meets the x-axis i.e. (1,0).
-
-
The next vertex will be the origin. Click on (0,0)
-
The final vertex will be on the y-axis.
-
Click on the Perpendicular Line tool.
-
Click on point A.
-
Click on the y-axis. A horizontal line appears
-
Using the New Point tool, click on the point where this horizontal line meets the y-axis i.e. (0,1).
-
-
To draw the square, change to the Polygon tool, and click on points A, B, C, D and then point A again.
-
Change to the Move tool and slide the slider. The size of the square should change.
-
Complete this table of values:
-
What is the constant of proportionality between the perimeter and the side length?
-
Type ‘A = (2a,a)’ into the input box and press Enter. Slide the slider.
-
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.)
-
-
What is the constant of proportionality between the perimeter and the smaller side length of the rectangle?
-
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?