We assume that:
0. the original figure is the bigger figure, in grey,
,
1. the final figure is the smaller figure, in blue.
1) Original figure
From the graph, we see that the shortest side has a length of 1 unit.
2) Final figure
From the graph, we see that the position of the :
• original figure is x = 2,
,
• final figure is x' = 1/2.
From these observations, we conclude that the scale factor r of the dilatation is 1/4, because:
[tex]x^{\prime}=r\cdot x\Rightarrow r=\frac{x^{\prime}}{x}=\frac{\frac{1}{2}}{2}=\frac{1}{4}\text{.}[/tex]
We found that the size of the shortest size of the original figure was y = 1 unit, the shortest size of the final figure is:
[tex]y^{\prime}=r\cdot y=\frac{1}{4}\cdot1=\frac{1}{4}=0.25.[/tex]
Answer
(a)
• The shortest side length of the original figure ,1, units,
,
• The shortest side length of the final figure ,0.25, units,
