Question

May I please get help with recreating the dilation for I have tried multiple times but still could not get the correct way

Answer 1

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:

`x^(\prime)=r\cdot x\Rightarrow r=(x^(\prime))/(x)=((1)/(2))/(2)=(1)/(4)\text{.}`

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:

`y^(\prime)=r\cdot y=(1)/(4)\cdot1=(1)/(4)=0.25.`

Answer

(a)

• The shortest side length of the original figure ,1, units,

,

• The shortest side length of the final figure ,0.25, units,