Question

I’m trying to find the rule of transformations and then preserving the length and angle measure of coordinate notation.

Answer 1

For part (5), to identify the rule, we must take note of the following rules for rotation about the origin.

`\begin{gathered} 90\degree\colon(x,y)\rightarrow(-y,x) \\ 180\degree\colon(x,y)\rightarrow(-x,-y) \\ 270\degree\colon(x,y)\rightarrow(y,-x) \end{gathered}`

Since each coordinate of the pre-image is negated, we can say that the image was rotated 180° about the origin. This is 180° rotation.

`180\degree\colon(x,y)\rightarrow(-x,-y)`

Since it is rotation, the object is only rotated about the origin without changing the shape and the size of the image. Thus, we can say that the lengths and the angles are preserved.

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For part (6), notice that the image was moved 1 unit to the right and then 2 units downward. Thus, the following rule was used.

`(x,y)\rightarrow(x+1,y-2)`

This means that each coordinated is translated 1 unit to the right (1 is added to each x-coordinate) and 2 units downward (2 is subtracted to each y-coordinate). This is translation.

Since the image is only translated, this means that the size and shape did not change. Thus, the angles and the lengths of the image were also preserved.