Rule for the first transformation : (x, y) → (2.5x, 2.5y)
Rule for the second transformation : (x, y) → [(x - 4), (y + 1)]
Transformations of a figure:
- If a figure is dilated by a scale factor 'k', rule defining the dilation will be,
[tex]k=\frac{\text{Dimension of the image circle}}{\text{Dimension of the preimage circle}}[/tex]
- If a point (x, y) is shifted 'a' units left and 'b' units upwards,
Rule defining the translation will be,
(x, y) → (x - a, y + b)
From the picture attached,
Radius of image circle = 2.5 units
Radius of preimage circle = 1 unit
Scale factor 'k' = [tex]\frac{2.5}{1}[/tex]
= 2.5
Since, image circle (blue) is shifted to the left and upwards, rule for the translation will be,
(x, y) → [(x - a), (y + b)]
Following the rule, coordinates of the image circle will be,
(0, 0) → [(0 - a), (0 + b)]
→ (-a, b)
Coordinates of the image circle from the picture → (-4, 1)
Therefore, -a = -4 ⇒ a = 4
b = 1
First transformation: (x, y) → (2.5x, 2.5y)
Second transformation : (x, y) → [(x - 4), (y + 1)]
Learn more about the transformations here,
https://brainly.com/question/11709244?referrer=searchResults
