Question

Define each of the 4 transformations listed below. Explain what happens to an image when you apply each of the transformations:(x,y) -> (3/8x, 3/8y)(x,y) -> (8/3x, 8/3y)(x,y) -> (x + 5, y + 5)(x,y) -> (x - 5, y - 5)

Answer 1

(1)

`\begin{gathered} (x,y)\rightarrow((3)/(8)x,(3)/(8)y) \\ \text{This is a dilation},\text{ and this means the image has been dilated by a factor of }(3)/(8) \\ \text{When this transformation is applied the image reduces in size} \end{gathered}`

(2)

`\begin{gathered} (x,y)\rightarrow((8)/(3)x,(8)/(3)y) \\ \text{This too is a dilation and the image has b}en\text{ dilated by a factor of }(8)/(3) \\ \text{When this transformation is applied the image increases in size} \end{gathered}`

(3)

`\begin{gathered} (x,y)\rightarrow(x+5,y+5) \\ This\text{ is a translation and the coordinates of the image has been moved } \\ To\text{ the right of the x axes and upward on the y axes} \\ \text{When this transformation is applied the image moves upwards and towards the right side} \\ In\text{ other words, the image changes location} \end{gathered}`

(4)