Visualizing Area Change Factors
This applet allows you to see animations of scaling an object in 2 dimensions. Its goal is to reinforce the idea that area is affected by multiplying by the square of the length scale factor, which is the same as multiplying by the length scale factor twice. This applet shows that a similarity transformation consists of a horizontal and a vertical transformation, each of which multiply the area by the length scale factor.
To use this applet, first set the length scale factor to 2 or 3. Scale in the horizontal and then the vertical direction (or vice versa), and note the effect on the area. To reset the applet, reload the page, or set the scale factor to 1 and scale in both directions until the yellow and blue quadrilaterals are identical.
Notice the effect of scaling on area: With scale factor 2: Area after scaling in one direction = 2 x (original area) Area after scaling in both directions = 2 x 2 x (original area) Area change factor = 2 x 2 for this example |